<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  Schedule 13D


               UNDER THE SECURITIES EXCHANGE ACT OF 1934

                             National-Oilwell, Inc.
- --------------------------------------------------------------------------------
                                (Name of Issuer)

                          Common Stock, $.01 par value
- --------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                   637071 10 1
- --------------------------------------------------------------------------------
                                 (CUSIP Number)

   Thomas R. Denison, First Reserve Corporation, 1801 California Suite 4110,
                        Denver, CO 80202, (303) 382-1270
- --------------------------------------------------------------------------------
           (Name, Address and Telephone Number of Person Authorized to
                      Receive Notices and Communications)

                                    9/18/98
- --------------------------------------------------------------------------------
             (Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this 
schedule because of Rule 13d-1(e), 13d-1(f) or 13d-1(g), check the following 
box / /.

Note: Schedules filed in paper format shall include a signed original and five
copies of the schedule, including all exhibits. See Rule 13d-7(b) for other
parties to whom copies are to be sent.

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).

<PAGE>   2
                                  SCHEDULE 13D

CUSIP NO. 637071 10 1                                         PAGE 2 OF 27 PAGES

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
    
    First Reserve Fund V, Limited Partnership
    I.R.S. No.: 06-1295657
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

    N/A
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


    Delaware
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          334,830
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                                        
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    334,830
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     334,830     
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES*                                                        [X]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     0.6%
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     PN
- --------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7 
      (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.


<PAGE>   3
                                  SCHEDULE 13D

CUSIP NO. 637071 10 1                                         PAGE 3 OF 27 PAGES

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
    
    First Reserve Fund V-2, Limited Partnership
    I.R.S. No.: 06-635-1960
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

    N/A
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


    Delaware
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          334,830
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                                        
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    334,830
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     334,830  
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES*                                                        [X]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     0.6%
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     PN
- --------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.  


<PAGE>   4
                                  SCHEDULE 13D

CUSIP NO. 637071 10 1                                         PAGE 4 OF 27 PAGES

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
    
    First Reserve Fund VI, Limited Partnership
    I.R.S. No.: 06-1334650
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

    N/A
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


    Delaware
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          7,700,834
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                                        
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    7,700,834
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     7,700,834     
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES*                                                        [X]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     14.5%
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     PN
- --------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7  
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.  


<PAGE>   5
                                  SCHEDULE 13D

CUSIP NO. 637071 10 1                                         PAGE 5 OF 27 PAGES

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
    
    First Reserve Fund VII, Limited Partnership
    I.R.S. No.: 06-1457408
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

    OO
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


    Delaware
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          979,100       
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                                        
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    979,100
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     979,100
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES*                                                        [X]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     1.9%
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     PN
- --------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7   
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.  


<PAGE>   6
                                  SCHEDULE 13D

CUSIP NO. 637071 10 1                                         PAGE 6 OF 27 PAGES

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
    
    First Reserve Fund VIII, LP
    I.R.S. No.: 06-1507364
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

    OO
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


    Delaware
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          979,100       
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                                        
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    979,100       
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     979,100            
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES*                                                        [X]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     1.9%    
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     PN
- --------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.  


<PAGE>   7
                                  SCHEDULE 13D

CUSIP NO. 637071 10 1                                         PAGE 7 OF 27 PAGES

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
    
    First Reserve GP VII, LP
    I.R.S. No.: 06-1520256
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

    N/A
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


    Delaware
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          979,100       
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                                        
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    979,100       
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     979,100            
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES*                                                        [X]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     1.9%    
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     PN
- --------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.  


<PAGE>   8
                                  SCHEDULE 13D

CUSIP NO. 637071 10 1                                         PAGE 8 OF 27 PAGES

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
    
    First Reserve GP VIII, LP
    I.R.S. No.: 06-1507318
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

    N/A
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


    Delaware
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          979,100       
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                                        
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    979,100       
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     979,100            
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES*                                                        [X]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     1.9%    
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     PN
- --------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.  


<PAGE>   9
                                  SCHEDULE 13D

CUSIP NO. 637071 10 1                                         PAGE 9 OF 27 PAGES

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
    
    First Reserve Corporation
    I.R.S. No.: 06-1210123
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

    N/A
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


    Delaware
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          10,328,694       
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                                        
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    10,328,694       
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     10,328,694            
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES*                                                        [ ]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     19.5%    
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     CO
- --------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7 
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.  


<PAGE>   10
                                  SCHEDULE 13D

CUSIP NO. 637071 10 1                                        PAGE 10 OF 27 PAGES

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
    
    William E. Macaulay
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

    N/A
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


    USA
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           1,333
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          10,328,694       
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    1,333                    
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    10,328,694       
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     10,330,027            
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES*                                                        [ ]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     19.5%    
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     IN
- --------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7   
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.  


<PAGE>   11
                                  SCHEDULE 13D

CUSIP NO. 637071 10 1                                        PAGE 11 OF 27 PAGES

- --------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
    
    John A. Hill
- --------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3   SEC USE ONLY


- --------------------------------------------------------------------------------
4   SOURCE OF FUNDS*

    N/A
- --------------------------------------------------------------------------------
5   CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
    TO ITEMS 2(d) OR 2(e)                                                   [ ]

- --------------------------------------------------------------------------------
6   CITIZENSHIP OR PLACE OF ORGANIZATION


    USA
- --------------------------------------------------------------------------------
                7   SOLE VOTING POWER
  NUMBER OF
   SHARES           
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          10,328,694       
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                                        
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    10,328,694       
- --------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     10,328,694            
- --------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES 
     CERTAIN SHARES*                                                        [ ]

- --------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

     19.5%    
- --------------------------------------------------------------------------------
14   TYPE OF REPORTING PERSON*

     IN
- --------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.  


<PAGE>   12
ITEM 1.  SECURITY AND ISSUER.

         This Statement on Schedule 13D (the "Schedule 13D") relates to the
Common Stock, par value $0.01 per share (the "Common Stock"), of
National-Oilwell, Inc., a Delaware corporation ("National-Oilwell" or the
"Company"). The principal executive offices of the Company are located at 5555
San Felipe, Houston, Texas 77056.

ITEM 2.  IDENTITY AND BACKGROUND.

         This Schedule 13D is being filed jointly by First Reserve Fund V,
Limited Partnership ("Fund V"), First Reserve Fund V-2, Limited Partnership
("Fund V-2"), First Reserve Fund VI, Limited Partnership ("Fund VI"), First
Reserve Fund VII, Limited Partnership ("Fund VII"), First Reserve Fund VIII, LP
("Fund VIII", and collectively, with Fund V, Fund V-2, Fund VI and Fund VII, the
"Funds"), First Reserve GP VII, LP, ("GP VII"), First Reserve GP VIII, LP ("GP
VIII"), First Reserve Corporation ("First Reserve"), William E. Macaulay and
John A. Hill to report the acquisition by Fund VII and Fund VIII of Common
Stock. GP VII and GP VIII are the general partners of Fund VII and Fund VIII,
respectively. First Reserve is the sole general partner of Fund V, Fund V-2,
Fund VI, GP VII and GP VIII. The Funds, in the aggregate, directly own more than
5% of the issued and outstanding shares of Common Stock.

         The Funds are Delaware limited partnerships and their principal purpose
is to make equity, equity-linked and debt investments in companies engaged in
various energy and energy related activities.

         GP VII and GP VIII are Delaware limited partnerships which are the
general partner of Fund VII and Fund VIII, respectively. First Reserve is a
Delaware corporation and is the general partner of Fund V, Fund VI, Fund V-2, GP
VII and GP VIII. The principal business of First Reserve is to provide
investment management services to the Funds and to other investment funds
managed by First Reserve.

                                                             PAGE 12 of 27 PAGES

<PAGE>   13

         The principal business and office address of First Reserve, GP VII, GP
VIII, each of the Funds, Mr. Macaulay and Mr. Hill (together, the "Reporting
Persons") is 475 Steamboat Road, Greenwich, Connecticut 06830.

         Information with respect to the executive officers and directors of
First Reserve, including name, business address, present principal occupation or
employment and the organization in which such employment is conducted, and their
citizenship is listed on the attached Schedule I, which is incorporated in this
Schedule 13D by reference.

         During the last five years, none of the Reporting Persons nor any
executive officer or director of First Reserve has (i) been convicted in a
criminal proceeding (excluding traffic violations or similar misdemeanors) or
(ii) been a party to a civil proceeding or a judicial or administrative body of
competent jurisdiction and as a result of such proceeding was or is subject to a
judgment, decree or final order enjoining future violations of, or prohibiting
or mandating activities subject to, federal or state securities laws or finding
any violation with respect to such laws.

ITEM 3     SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.

         The source of funds for the Funds' acquisition of beneficial ownership
of the Common Stock is money contributed by limited and general partners for
investment by the Funds. Except in relation to its partnership interest in the
Funds, no funds were acquired directly by GP VII, GP VIII, or First Reserve for
their indirect acquisition of beneficial ownership of the Common Stock.


                                                             PAGE 13 OF 27 PAGES

<PAGE>   14


ITEM 4.    PURPOSE OF TRANSACTION.

         Prior to the company going public on October 28, 1996, Fund V, Fund V-2
and Fund VI owned 167,415, 167,415 and 3,850,417 shares of Common Stock,
respectively. Due to a 2 for 1 stock split, Fund V, Fund V-2 and Fund VI now own
334,830, 334,830 and 7,700,834 shares of Common Stock, respectively. Fund V,
Fund V-2, Fund VI and First Reserve filed a Schedule 13G on February 14, 1997.
All shares of Common Stock acquired by the Funds, including the shares acquired
by Fund VII and Fund VIII and disclosed in Item 5 of this Schedule 13D were
acquired for investment purposes.

         The Funds intend to participate in and influence the affairs of the
Company through the exercise of their voting rights with respect to the shares
of Common Stock owned by the Funds. Two officers of First Reserve (William E.
Macaulay and Bruce R. Rothstein) currently serve as directors of the Company.

         The Funds and First Reserve intend to review on a continuing basis the
Funds' investment in the Company and may or may not purchase additional shares,
on the open market or otherwise, subject to: the price and availability of the
Company's securities; subsequent developments affecting the energy market as a
whole, the Company and the Company's business and prospects; other investment
and business opportunities available to the Funds; general stock market and
economic conditions; and other factors.


                                                             PAGE 14 OF 27 PAGES

<PAGE>   15

         Fund VII and Fund VIII each filed a Notification and Report Form under
the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended, with the
Federal Trade Commission and the United States Department of Justice stating an
intention to purchase at least $15 million of the Company's Common Stock. Fund
VIII's filing further stated that it may, upon consultation with the Company and
depending upon market conditions, purchase over 15% of the outstanding shares of
the Company's Common Stock. First Reserve and the Funds do not have any
commitment to make those purchases and may, based on any of the factors listed
above, decide not to make such additional purchases. First Reserve and the Funds
may also decide to dispose of Company securities at any time or to formulate
other purposes, plans or proposals regarding the Company or any of its
securities.


ITEM 5.  INTEREST IN SECURITIES OF THE ISSUER.

         (a) As of September 25, 1998, the Funds beneficially owned an aggregate
of 10,328,694 shares of Common Stock, constituting approximately 19.5% of the
52,996,785 shares of Common Stock outstanding as of August 12, 1998 as reported
by the Company.

         GP VII and GP VIII as the general partner of Fund VII and Fund VIII may
be deemed to beneficially own the shares of Common Stock owned by those
respective Funds. First Reserve as the general partner of Fund V, Fund V-2, Fund
VI, GP VII and GP VIII may be deemed to beneficially own all shares of Common
Stock owned by the Funds. Mr. Macaulay and Mr. Hill may be deemed to share
beneficial ownership of the shares beneficially owned by the Funds as a result
of their ownership of and control over First Reserve. Mr. Macaulay and Mr. Hill
disclaim beneficial ownership of such shares. Except as set forth otherwise in
this Schedule 13D, neither the filing of this Schedule nor any of its contents
shall be deemed to constitute an admission that Mr. Macaulay or Mr. Hill is the


                                                             PAGE 15 OF 27 PAGES



<PAGE>   16


beneficial owner of the Common Stock referred to in this paragraph for purposes
of Section 13(d) of the Exchange Act or for any other purpose, and such
beneficial ownership is expressly disclaimed.

         The number and percentage of shares of Common Stock beneficially owned
by each Reporting Person are as follows:

<TABLE>
<CAPTION>
                                                                                            Percentage of Shares
                                                                                              of Common Stock
                                                                                              Outstanding on
                                                                     Shares                   August 12, 1998
                                                                     ------                 --------------------

<S>                                                                 <C>                               <C>
Fund V                                                              334,830                           .6%

Fund V-2                                                            334,830                           .6%

Fund VI                                                           7,700,834                         14.5%

Fund VII                                                            979,100                          1.9%

Fund VIII                                                           979,100                          1.9%

GP VII (through Fund VII)                                           979,100                          1.9%

GP VIII (through Fund VIII)                                         979,100                          1.9%

First Reserve (through the Funds)                                10,328,694                          19.5%

William E. Macaulay*                                             10,330,027                          19.5%

John A. Hill*                                                    10,328,694                          19.5%
</TABLE>


*  10,328,694 of the shares reported as beneficially owned by Mr. Macaulay and
   all of the shares reported as beneficially owned by Mr. Hill are directly 
   owned by the Funds. Mr. Macaulay and Mr. Hill disclaim beneficial ownership 
   of such shares.


         (b) Each Fund shares with its general partner the power to vote or to
direct the vote of the shares directly held by it. GP VII and GP VIII, in their
roles as general partners of Fund VII and Fund VIII, respectively, and First
Reserve, in its role as general partner Fund V, Fund V-2 and Fund VI, and of GP
VII and GP VIII, share with each Fund the power to cause each Fund to dispose of


                                                             PAGE 16 OF 27 PAGES

<PAGE>   17

or vote the shares of Common Stock directly held by such Fund. As a result of
their positions with and ownership interest in First Reserve, Mr. Macaulay and
Mr. Hill may be deemed to have shared power to direct the voting and disposition
of all 10,328,694 shares of Common Stock held directly by the Funds. Mr.
Macaulay also owns options to purchase 1,333 shares of Common Stock and has sole
voting and dispositive power over these shares.

         (c) The following routine brokerage transactions have been made by the
Reporting Persons in the previous 60 days:

                  (1)      Purchases by Fund VII:


<TABLE>
<CAPTION>
                                                                                          DOLLAR AMOUNT
TRADE DATE                    SHARES                        PRICE PER SHARE                OF PURCHASE
- ----------                    ------                        ---------------               -------------
<S>                             <C>                         <C>                          <C>           
9/3/98                          25,000                      $  9.0938                    $   227,345.00

9/4/98                          12,250                          9.25                         113,312.50

9/9/98                         111,350                         10.3660                     1,154,254.10

9/10/98                            500                         10.3125                         5,156.25

9/14/98                         97,100                         12.1250                     1,177,337.50

9/15/98                         76,950                         12.6931                       976,734.05

9/17/98                         90,800                         12.5000                     1,135,000.00

9/18/98 **                     250,000                         12.4983                     3,124,575.00

9/22/98                        164,000                         11.8415                     1,942,006.00
</TABLE>



                                                             PAGE 17 OF 27 PAGES

<PAGE>   18


<TABLE>
<CAPTION>
                                                                                          DOLLAR AMOUNT
TRADE DATE                    SHARES                        PRICE PER SHARE                OF PURCHASE
- ----------                    ------                        ---------------               -------------
<S>                            <C>                         <C>                          <C>           
9/23/98                         72,650                         12.2037                       886,598.81

9/24/98                         78,500                         12.0096                       942,753.60

Total Purchases in the
past 60 days
</TABLE>


                  (2)      Purchases by Fund VIII:


<TABLE>
<CAPTION>
                                                                                          DOLLAR AMOUNT
TRADE DATE                    SHARES                        PRICE PER SHARE                OF PURCHASE
- ----------                    ------                        ---------------               -------------
<S>                             <C>                         <C>                          <C>           
9/3/98                         25,000                      $  9.0938                    $   227,345.00

9/4/98                         12,250                         9.25                          113,312.50

9/9/98                        111,350                        10.3660                      1,154,254.10

9/10/98                           500                        10.3125                          5,156.25

9/14/98                        97,100                        12.1250                      1,177,337.50

9/15/98                        76,950                        12.6931                        976,734.05

9/17/98                        90,800                        12.5000                      1,135,000.00

9/18/98 **                    250,000                        12.4983                      3,124,575.00

9/22/98                       164,000                        11.8415                      1,942,006.00

9/23/98                        72,650                        12.2037                        886,598.81
</TABLE>



                                                             PAGE 18 OF 27 PAGES

<PAGE>   19


<TABLE>
<CAPTION>
                                                                                          DOLLAR AMOUNT
TRADE DATE                    SHARES                        PRICE PER SHARE                OF PURCHASE
- ----------                    ------                        ---------------               -------------
<S>                            <C>                         <C>                          <C>           
9/24/98                        78,500                        12.0096                        942,753.60

Total purchases in the
past 60 days
</TABLE>


         ** With the transactions on this date the Reporting Persons crossed the
2% threshold for acquisitions within the preceding 12 months and became subject
to reporting under Section 13(d) of the Securities and Exchange Act.

         (d) To the best knowledge of the Reporting Persons, no other person has
the right to receive, or the power to direct the receipt of dividends from, or
the power to direct the receipt of proceeds of the sale of the shares of Common
Stock owned by the Reporting Persons.

         (e)      Not applicable.

ITEM 6.  CONTRACTS, ARRANGEMENTS OR UNDERSTANDING WITH RESPECT TO SECURITIES OF
         THE ISSUER.

         A Joint Filing Agreement dated September 28, 1998, by and between the
Funds, GP VII, GP VIII, First Reserve, William E. Macaulay and John A. Hill, has
been executed by the Reporting Persons. A copy of that Agreement is attached
hereto as Exhibit A and incorporated herein by reference. In addition, Fund V,
Fund V-2, and Fund VI are parties to a Stockholders Agreement, dated January 16,
1996, by and amount the Company, such Funds and other stockholders, pursuant to
which such Funds have certain registration rights with respect to the shares of
Common Stock held by such Funds. That Stockholders Agreement is incorporated by
reference as Exhibit B to this Schedule 13D. Except as set forth in this
Schedule 13D, the Reporting Persons do




<TABLE>
<CAPTION>
                                                                                          DOLLAR AMOUNT
TRADE DATE                    SHARES                        PRICE PER SHARE                OF PURCHASE
- ----------                    ------                        ---------------               -------------
<S>                            <C>                         <C>                          <C>           
9/23/98                         72,650                         12.2037                       886,598.81

9/24/98                         78,500                         12.0096                       942,753.60

Total Purchases in the
past 60 days
</TABLE>


                  (2)      Purchases by Fund VIII:


<TABLE>
<CAPTION>
                                                                                          DOLLAR AMOUNT
TRADE DATE                    SHARES                        PRICE PER SHARE                OF PURCHASE
- ----------                    ------                        ---------------               -------------
<S>                             <C>                         <C>                          <C>           
9/3/98                         25,000                      $  9.0938                    $   227,345.00

9/4/98                         12,250                         9.25                          113,312.50

9/9/98                        111,350                        10.3660                      1,154,254.10

9/10/98                           500                        10.3125                          5,156.25

9/14/98                        97,100                        12.1250                      1,177,337.50

9/15/98                        76,950                        12.6931                        976,734.05

9/17/98                        90,800                        12.5000                      1,135,000.00

9/18/98 **                    250,000                        12.4983                      3,124,575.00

9/22/98                       164,000                        11.8415                      1,942,006.00

9/23/98                        72,650                        12.2037                        886,598.81
</TABLE>



                                                             PAGE 19 OF 27 PAGES

<PAGE>   20

not have any contracts, arrangements, understandings, or relationships with
respect to any securities of the Company.

ITEM 7.  MATERIAL TO BE FILED AS EXHIBITS.

         Exhibit A.  Agreement Concerning Joint Filing of Schedule 13D.

         Exhibit B. Stockholders Agreement, dated January 16, 1996, by and among
the Company, Fund V, Fund V-2, Fund VI and other stockholders of the Company
(incorporated by reference from Form S-1 filed by National-Oilwell, Inc. on
August 29, 1996, Registration Number 333-11051)


                                                             PAGE 20 OF 27 PAGES


<PAGE>   21




                                    SIGNATURE

         After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this Statement is true, complete and
correct.

  Dated:  September 28, 1998.
                               FIRST RESERVE FUND V, LIMITED
                               PARTNERSHIP
                               By:  First Reserve Corporation,
                                      as General Partner



                                     By: /s/ THOMAS R. DENISON  
                                         --------------------------------------
                                         Name:  Thomas R. Denison
                                         Title: Managing Director





                               FIRST RESERVE FUND V-2, LIMITED
                               PARTNERSHIP

                               By:  First Reserve Corporation,
                                      as General Partner



                                     By: /s/ THOMAS R. DENISON 
                                         --------------------------------------
                                         Name:  Thomas R. Denison
                                         Title: Managing Director






                               FIRST RESERVE FUND VI, LIMITED
                               PARTNERSHIP

                               By:  First Reserve Corporation,
                                      as General Partner



                                     By: /s/ THOMAS R. DENISON 
                                         --------------------------------------
                                         Name:  Thomas R. Denison
                                         Title: Managing Director



                                                             PAGE 21 OF 27 PAGES

<PAGE>   22
\
                               FIRST RESERVE FUND VII, LIMITED
                               PARTNERSHIP

                               By:  First Reserve GP VII, LP, as General Partner
                                    By:  First Reserve Corporation,
                                           as General Partner


                                     By: /s/ THOMAS R. DENISON 
                                         --------------------------------------
                                         Name:  Thomas R. Denison
                                         Title: Managing Director





                               FIRST RESERVE FUND VIII, LP

                               By:  First Reserve GP VIII, LP,
                                      as General Partner
                                    By:  First Reserve Corporation,
                                           as General Partner


                                     By: /s/ THOMAS R. DENISON 
                                         --------------------------------------
                                         Name:  Thomas R. Denison
                                         Title: Managing Director




                               FIRST RESERVE GP VII, LP

                               By:  First Reserve Corporation,
                                      as General Partner


                                     By: /s/ THOMAS R. DENISON 
                                         --------------------------------------
                                         Name:  Thomas R. Denison
                                         Title: Managing Director


                                                             PAGE 22 OF 27 PAGES


<PAGE>   23
                               FIRST RESERVE GP VIII, LP

                               By:  First Reserve Corporation,
                                      as General Partner


                                     By: /s/ THOMAS R. DENISON 
                                         --------------------------------------
                                         Name:  Thomas R. Denison
                                         Title: Managing Director





                                FIRST RESERVE CORPORATION


                                By:  /s/ THOMAS R. DENISON
                                     ------------------------------------------ 
                                     Name:  Thomas R. Denison
                                     Title: Managing Director



                                /s/ WILLIAM E. MACAULAY
                                ------------------------------------------
                                William E. Macaulay



                                /s/ JOHN A. HILL
                                ------------------------------------------
                                John A. Hill


                                       
                                                             PAGE 23 OF 27 PAGES

<PAGE>   24




                                   Schedule I

         1. The name, business address, and present principal occupation or
employment of each of the executive officers and directors of the First Reserve
Corporation are set forth below. Unless otherwise indicated, (i) the business
address of each is 475 Steamboat Road, Greenwich, Connecticut 06830, (ii) each
such person is a citizen of the United States, and (iii) such person does not
have any other principal occupation:

                           Name and Position with
                           First Reserve Corporation
                           --------------------------
  
         William E. Macaulay
         Chairman and Chief Executive Officer, Managing Director and Director

         John A. Hill
         Vice-Chairman, Managing Director and Director

         David H. Kennedy
         Managing Director and Director

         Jonathan S. Linker
         Managing Director

         Thomas R. Denison
         Managing Director, General Counsel, and Assistant Secretary

         Cathleen M. Ellsworth
         Managing Director

         Elizabeth C. Foley
         Managing Director, Treasurer and Secretary

         Bruce M. Rothstein
         Managing Director

         Jennifer G. Kornfield
         Vice President and Controller


                                                                   PAGE 24 OF 27



<PAGE>   25




                                  EXHIBIT INDEX


<TABLE>
<CAPTION>
     Exhibit                            Description                                          Page
     -------                            -----------                                          ----

<S>                <C>                                                                      <C>
        A          Agreement Concerning Joint Filing of Schedule 13D

        B          Stockholders Agreement, dated January 16, 1996, by and among
                   the Company, Fund V, Fund V-2, Fund VI and other stockholders
                   of the Company (incorporated by reference from Form S-1 filed
                   by National-Oilwell, Inc. on August 29, 1996, Registration
                   Number 333-11051)
</TABLE>



                                       14





<PAGE>   1

                             JOINT FILING AGREEMENT


         We, the signatories of the statement on Schedule 13D filed with respect
to the Common Stock of National-Oilwell, Inc., to which this Agreement is
attached, hereby agree that such statement is, and any amendments thereto filed
by any of us will be, filed on behalf of each of us pursuant to and in
accordance with the provisions of Rule 13d-1(k) of the Securities Exchange Act
of 1934.

                                    FIRST RESERVE FUND V, LIMITED 
                                    PARTNERSHIP
                                    By:  First Reserve Corporation,
                                             as General Partner



                                    By: /s/ Thomas R. Denison
                                       ---------------------------------
                                         Name:  Thomas R. Denison
                                         Title:  Managing Director





                                    FIRST RESERVE FUND V-2, LIMITED 
                                    PARTNERSHIP

                                    By:  First Reserve Corporation,
                                             as General Partner



                                    By: /s/ Thomas R. Denison
                                       ---------------------------------
                                         Name:  Thomas R. Denison
                                         Title:  Managing Director





                                    FIRST RESERVE FUND VI, LIMITED 
                                    PARTNERSHIP

                                    By:  First Reserve Corporation,
                                             as General Partner



                                    By: /s/ Thomas R. Denison
                                       ---------------------------------
                                         Name:  Thomas R. Denison
                                         Title:  Managing Director




                                                             PAGE 25 OF 27 PAGES

<PAGE>   2

                                FIRST RESERVE FUND VII, LIMITED 
                                PARTNERSHIP


                                By: First Reserve GP VII, Limited Partnership
                                         as General Partner
                                By:  First Reserve Corporation,
                                         as General Partner



                                By: /s/ Thomas R. Denison
                                   --------------------------------------
                                     Name:  Thomas R. Denison
                                     Title:  Managing Director





                                FIRST RESERVE FUND VIII, LP


                                By:  First Reserve GP VII, Limited Partnership
                                         as General
 Partner,
                                By:      First Reserve Corporation
                                         as General Partner




                                By: /s/ Thomas R. Denison
                                   --------------------------------------
                                     Name:  Thomas R. Denison
                                     Title:  Managing Director




                                FIRST RESERVE GP VII, LP

                                By:  First Reserve Corporation,
                                         as General Partner



                                By: /s/ Thomas R. Denison
                                   --------------------------------------
                                     Name:  Thomas R. Denison
                                     Title:  Managing Director




                                                             PAGE 26 OF 27 PAGES

<PAGE>   3




                                FIRST RESERVE GP VIII, LP

                                By:  First Reserve Corporation,
                                         as General Partner



                                By: /s/ Thomas R. Denison
                                   --------------------------------------
                                     Name:  Thomas R. Denison
                                     Title:  Managing Director



                                FIRST RESERVE CORPORATION



                                By: /s/ Thomas R. Denison
                                   --------------------------------------
                                     Name:  Thomas R. Denison
                                     Title:  Managing Director





                                WILLIAM E. MACAULAY




                                By: /s/ William E. Macaulay
                                   --------------------------------------
                                     Name:  William E. Macaulay


                                JOHN A. HILL




                                By: /s/ John A. Hill
                                   --------------------------------------
                                     Name:  John A. Hill


                                                             PAGE 27 OF 27 PAGES