<PAGE>   1
                                  SCHEDULE 13D
                                 (Rule 13d-101)

                  SECURITIES AND EXCHANGE COMMISSION
                        WASHINGTON, D.C. 20549

               Under the Securities Exchange Act of 1934
                            Amendment No.   7
                                         --------

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

                                  Common Stock
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

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


<TABLE>
<S>    <C>
Thomas R. Denison - First Reserve Corporation, 1801 California St., #4110, Denver, CO 80202, (303) 382-1270
-----------------------------------------------------------------------------------------------------------
      (Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)
</TABLE>


                                December 19, 2000
--------------------------------------------------------------------------------
             (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
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

CUSIP NO. 637071 10 1                                        PAGE 2 OF 11 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) [X]
                                                                         (b) [ ]

--------------------------------------------------------------------------------
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           0        
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          7,231,532
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    0
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    
--------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     7,231,532
--------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
                                                                             [ ]
--------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 11

     9.0%
--------------------------------------------------------------------------------
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>   3

CUSIP NO. 637071 10 1                                        PAGE 3 OF 11 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) [X]
                                                                         (b) [ ]

--------------------------------------------------------------------------------
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           0        
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          3,461,334
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    0
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    3,461,334
--------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     3,461,334
--------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
                                                                             [ ]
--------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 11

     4.3%
--------------------------------------------------------------------------------
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

CUSIP NO. 637071 10 1                                        PAGE 4 OF 11 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) [X]
                                                                         (b) [ ]

--------------------------------------------------------------------------------
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           0        
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          1,548,600
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    0
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    1,548,600                    
--------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     1,548,600
--------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
                                                                             [ ]
--------------------------------------------------------------------------------
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>   5

CUSIP NO. 637071 10 1                                        PAGE 5 OF 11 PAGES

--------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    First Reserve Fund VIII, L.P.
    I.R.S. No.: 06-1507364
--------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                    (a) [X]
                                                                         (b) [ ]

--------------------------------------------------------------------------------
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           0        
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          2,209,100
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    0
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    2,209,100
--------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     2,209,100
--------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
                                                                             [ ]
--------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 11

     2.8%
--------------------------------------------------------------------------------
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

CUSIP NO. 637071 10 1                                        PAGE 6 OF 11 PAGES

--------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    First Reserve GP VII, L.P.
    I.R.S. No.: 06-1520256
--------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                    (a) [X]
                                                                         (b) [ ]

--------------------------------------------------------------------------------
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           0        
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          1,548,600
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    0
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    1,548,600                    
--------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     1,548,600
--------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
                                                                             [ ]
--------------------------------------------------------------------------------
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

CUSIP NO. 637071 10 1                                        PAGE 7 OF 11 PAGES

--------------------------------------------------------------------------------
 
1   NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    First Reserve GP VIII, L.P.
    I.R.S. No.: 06-1507318
--------------------------------------------------------------------------------
2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                    (a) [X]
                                                                         (b) [ ]

--------------------------------------------------------------------------------
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           0        
BENEFICIALLY   -----------------------------------------------------------------
  OWNED BY      8   SHARED VOTING POWER
   EACH            
 REPORTING          2,209,100
  PERSON       -----------------------------------------------------------------
   WITH         9   SOLE DISPOSITIVE POWER

                    0
               -----------------------------------------------------------------
               10   SHARED DISPOSITIVE POWER
     
                    2,209,100
--------------------------------------------------------------------------------
11   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     2,209,100
--------------------------------------------------------------------------------
12   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
                                                                             [ ]
--------------------------------------------------------------------------------
13   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 11

     2.8%
--------------------------------------------------------------------------------
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

         This Amendment No. 7 to the statement on Schedule 13D (the
"Statement"), originally filed on September 28, 1998, is filed by First Reserve
Fund VI, Limited Partnership ("Fund VI"), First Reserve Fund VII, Limited
Partnership ("Fund VII"), First Reserve GP VII, L.P. ("GP VII"), First Reserve
Fund VIII, L.P. ("Fund VIII"), and First Reserve GP VIII, L.P. ("GP VIII," and
collectively, the "Funds"), and First Reserve Corporation ("First Reserve," and
together with the Funds, the "Reporting Persons") and relates to the Common
Stock, par value $0.01 per share (the "Common Stock"), of National-Oilwell,
Inc., a Delaware corporation (the "Issuer" or "National-Oilwell"). That Schedule
13D is hereby amended as set forth below.

ITEM 5.  INTEREST IN SECURITIES OF THE ISSUER.

         Item 5 is hereby deleted and replaced with the following:

         (a) As of the date hereof, the Reporting Persons beneficially owned an
aggregate of 7,231,532 shares of Common Stock which constitute approximately
9.0% of the 80,285,395 shares of Common Stock outstanding as of November 10,
2000, as reported by the Company.


<TABLE>
<CAPTION>
                                                               NUMBER OF SHARES                 PERCENTAGE OF
REPORTING PARTY                                               BENEFICIALLY OWNED                     CLASS
<S>                                                           <C>                               <C>
First Reserve Corporation (1), (2)                                  7,231,532                         9.0%

Fund VI                                                             3,461,334                         4.3%

Fund VII                                                            1,548,600                         1.9%

Fund VIII                                                           2,209,100                         2.8%

GP VII (2)                                                          1,548,600                         1.9%

GP VIII (2)                                                         2,209,100                         2.8%
</TABLE>


         (1) Consists of 7,219,034 shares of Common Stock held directly by First
Reserve and the Funds, and 9,950 shares underlying stock options issued to
William E. Macaulay and 2,548 shares underlying stock options issued to Ben A.
Guill in their capacity as directors of the Issuer. First Reserve may be deemed
to share dispositive and voting control over these shares.

         (2) GP VII and GP VIII are the general partners of Fund VII and Fund
VIII, respectively, and may be deemed to beneficially own the shares of Common
Stock owned by Fund VII and Fund VIII. First Reserve, as the general partner of
GP VII and GP VIII, may be deemed to beneficially own all of the shares of
Common Stock owned by the Funds.

         (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, as the general
partner of Fund VII, and GP VIII, as the general partner of Fund VIII, and First
Reserve, in its role as general partner of GP VII and GP VIII, shares with each
Fund the power to cause each Fund to dispose of or vote the shares of Common
Stock directly held by such Fund.

                                                                    Page 8 of 11

<PAGE>   9

         (c) The following transactions were effected during the past 60 days:


<TABLE>
<CAPTION>
REPORTING                                                   NUMBER OF
PARTY                               DATE                     SHARES                   PRICE               TRANSACTION
<S>                               <C>                       <C>                      <C>                  <C>

Fund VI                           11/21/2000                   55,600                $35.017              Common Sold

Fund VI                           12/19/2000                  613,500                $38.603              Common Sold

Fund VI                           12/20/2000                  122,800                $36.954              Common Sold
</TABLE>


         (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

                                                                    Page 9 of 11

<PAGE>   10



                                    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:  December 21, 2000.

                                          FIRST RESERVE CORPORATION



                                          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



                                          FIRST RESERVE FUND VII, LIMITED 
                                          PARTNERSHIP

                                          By: First Reserve GP VII, L.P.,
                                              as General Partner

                                              By: First Reserve Corporation,
                                                  as General Partner

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


                                                                   Page 10 of 11

<PAGE>   11





                                          FIRST RESERVE FUND VIII, L.P.

                                          By:  First Reserve GP VIII, L.P.,
                                               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, L.P.

                                          By: First Reserve Corporation,
                                              as General Partner

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


                                          FIRST RESERVE GP VIII, L.P.

                                          By: First Reserve Corporation,
                                              as General Partner

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


                                                                   Page 11 of 11