<PAGE>
 
                               UNITED STATES

                      SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                   FORM 10-Q
(Mark One)

    [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
                             EXCHANGE ACT OF 1934
                 For the quarterly period ended March 31, 1998

                                       OR

    [_] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
                              EXCHANGE ACT OF 1934

  For the transition period from___________to________________
  Commission File number 1-8158

                                        
                           VARCO INTERNATIONAL, INC.
            (Exact name of registrant as specified in its charter)

           California                                  95-0472620
  (State or other jurisdiction of          (I.R.S. Employer Identification No.)
  incorporation or organization)

                  743 North Eckhoff Street, Orange, Ca 92868
                   (Address of principal executive offices)
                                  (Zip code)

                                (714) 978-1900
             (Registrant's telephone number, including area code)
                                        
                                Not Applicable
(Former name, former address and former fiscal year, if changed since last
report)

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.  Yes  X    No
                                        ---      ---
                                  64,428,007

       (Number of shares of Common Stock outstanding at April 30, 1998)
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                         PART I-FINANCIAL INFORMATION
                                        
Item 1.  Financial Statements.

  Pursuant to General Instruction D to Form 10-Q, the Condensed Consolidated
Statements of Cash Flows, Condensed Consolidated Balance Sheets and Condensed
Consolidated Statements of Income of Varco International, Inc., (the "Company")
and its subsidiaries included in the registrant's First Quarter Report to
Shareholders for the three months ended March 31, 1998, filed as Exhibit 19
hereto are incorporated herein by reference.  Such financial statements should
be read in light of the following:

  Adjustments.  The financial statements contained in Exhibit 19 hereto include
all adjustments which in the opinion of management are of a normal recurring
nature, considered necessary to present fairly the results of operations for the
interim periods presented.

  Net Income Per Share.  Basic net income per share is based upon an average of
64,239,730 and 63,253,005 shares outstanding for the three months ended March
31, 1998, and 1997 respectively. Diluted net income per share is based upon an
average of 65,661,636 and  64,769,163 shares outstanding for the three months
ended March 31, 1998, and 1997 respectively.

  Inventories.  The Company estimates the components of inventory at March 31,
1998, and December 31, 1997, to be as follows:

<TABLE>
<CAPTION>
                           March 31, 1998       December 31, 1997
                           --------------       -----------------
<S>                        <C>                  <C>
   Raw Materials            $  5,946,000           $  6,118,000
   Work in Process            54,306,000             43,495,000
   Finished Goods            109,469,000             95,063,000
   LIFO Reserves             (12,027,000)           (12,705,000)
                            ------------           ------------
                            $157,694,000           $131,971,000
                            ============           ============
</TABLE>                                      
                                              
  Fixed Assets.  Fixed assets are stated net of accumulated depreciation of
$65,336,000 at March 31, 1998, and $62,469,000 at December 31, 1997.

  Common Stock and Additional Paid-In-Capital.  On March 31, 1998, the Company
Common Stock account was $54,702,000 and Additional Paid-In-Capital accounts
were $100,435,000.


Item 2.  Management's Discussion and Analysis of Financial Condition and Results
of Operations.

  Pursuant to General Instruction D to Form 10-Q, Management's Discussion and
Analysis of Financial Condition and Results of Operations contained in the
registrant's First Quarter Report to Shareholders for the three months ended
March 31, 1998, filed as Exhibit 19 hereto, is incorporated herein by reference.


                           PART II-OTHER INFORMATION
                                        
Item 2.  Changes in Securities

In July 1992 the Company sold $50.0 million aggregate principal amount of its
8.95% Senior Notes Due June 30, 1999 (the "Senior Notes") to a group of ten
institutional investors pursuant to a Note Agreement dated as of July 1, 1992
(as amended, the "Note Agreement"). The remaining

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$20.0 million principal balance of the Senior Notes is payable in two equal
installments on June 30, 1998 and June 30, 1999.

  The Note Agreement prohibits any "Restricted Payment" subsequent to July 17,
1992 unless after giving effect thereto, (i) the aggregate amount of all
Restricted Payments subsequent to such date would not exceed $5,000,000 plus the
cumulative sum of 50% of the Company's consolidated net income (or minus 100% in
the case of a deficit) subsequent to March 31, 1992 and (ii) the Company could
incur at least $1.00 of additional indebtedness under the Note Agreement
covenant limiting indebtedness. The term "Restricted Payment" includes (a) any
dividend (other than dividends payable in shares of capital stock) or other
distributions on any shares of capital stock of the Company; (b) any purchase,
redemption or other acquisition of any shares of the capital stock of the
Company or any rights or options to purchase or acquire such shares; and (c) any
"Restricted Investment", which is generally defined as any investment other than
an investment in a subsidiary of the Company or an investment in certain
designated government or rated securities. In addition, the Company may
purchase, redeem or otherwise acquire shares of its capital stock or make
Restricted Investments from the net cash proceeds of the substantially
concurrent sales of shares of capital stock or from the sale of securities
convertible into such shares upon conversion.

  On June 27, 1997 the Company entered into a seven-year unsecured revolving
credit agreement with three banks (the "Credit Agreement"). The Credit Agreement
provides for a credit facility of $65.0 million, inclusive of a $20.0 million
letter of credit sub-facility. The maximum available under the Credit Agreement
is reduced in equal quarterly amounts over the last four years of the Credit
Agreement.

  The Credit Agreement prohibits any "Restricted Junior Payment" unless (1) at
the time thereof no default exists under the Credit Agreement or will be caused
thereby and (2) the cumulative amount of all Restricted Junior Payments
subsequent to June 27, 1997, would not exceed the sum of $5,000,000 plus 25% of
the Company's consolidated net income arising after June 30, 1997. "Restricted
Junior Payment" is generally defined as (1) any dividend or other distribution
on any class of the Company's capital stock, except a dividend payable solely in
shares of that class; (2) any redemption, purchase or other acquisition for
value of any shares of any class of the capital stock of the Company; (3) any
payment made to retire or obtain the surrender of any outstanding warrants,
options or similar rights to acquire any shares of any class of the capital
stock of the Company; and (4) any payment on the Senior Notes other than
regularly scheduled payments of principal and interest thereon.
 

Item 6.  Exhibits and Reports on Form 8-K
 
    (a)  Exhibits
 
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  27.1   Financial Data Schedule March 31, 1998
 
  27.2   Restated Financial Data Schedule March 31, 1997
 
  27.3   Restated Financial Data Schedule June 30, 1997
 
  27.4   Restated Financial Data Schedule September 30, 1997


  (b)  Reports on Form 8-K.

       No reports on Form 8-K were filed during the quarter for which this
report is filed.

                                       4
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                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.


                                       VARCO INTERNATIONAL, INC.


Date: May 12, 1998                     By:  /s/ Richard A. Kertson
                                          ---------------------------
                                          Vice President-Finance
                                          and Chief Financial Officer



Date: May 12, 1998                     By:  /s/ Donald L. Stichler
                                          ---------------------------
                                          Vice President
                                          Controller-Treasurer and
                                          Secretary

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                                 EXHIBIT INDEX


  11    Statement re computation of per share earnings for the three months
        ended March 31, 1998 and 1997.


  19    Varco International, Inc. First Quarter Report to Shareholders, Three
        Months Ended March 31, 1998.

  27.1  Financial Data Schedule March 31, 1998
 
  27.2  Restated Financial Data Schedule March 31, 1997
 
  27.3  Restated Financial Data Schedule June 30, 1997
 
  27.4  Restated Financial Data Schedule September 30, 1997