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


                                 FORM 10-Q


  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                     1-13446
                       -------------------------------------------------------


                         Barrett Resources Corporation
--------------------------------------------------------------------------------
            (Exact name of registrant as specified in its charter)


             Delaware                                     84-0832476
--------------------------------------------------------------------------------
   (State or other jurisdiction of                    (I.R.S. Employer
   incorporation or organization)                     Identification No.)


1515 Arapahoe Street, Tower 3, Suite 1000  Denver, Colorado      80202
--------------------------------------------------------------------------------
      (Address of principal executive offices)                 (Zip Code)


                                (303) 572-3900
--------------------------------------------------------------------------------
             (Registrant's telephone number, including area code)


     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 
                                                  -----     -----     

     There were 31,724,839 shares of the registrant's $.01 par value common
stock outstanding as of May 7, 1998.
<PAGE>
 
                         BARRETT RESOURCES CORPORATION
                         -----------------------------


                                     INDEX
                                     -----



PART I.     FINANCIAL INFORMATION                                      PAGE
                                                                       ----


            Item 1.     Financial Statements

                        Consolidated Condensed Balance
                        Sheets - March 31, 1998 and
                        December 31, 1997..............................  3

                        Consolidated Condensed Statements of
                        Income - Three Months Ended
                        March 31, 1998 and 1997........................  4

                        Consolidated Condensed Statements of
                        Cash Flows - Three Months Ended
                        March 31, 1998 and 1997........................  5

            Item 2.     Management's Discussion and Analysis
                        of Financial Condition and Results
                        of Operations .................................  9


PART II.  OTHER INFORMATION

            Item 1.     Legal Proceedings.............................. 13
            Item 6.     Exhibits and Reports on Form 8-K............... 13
<PAGE>
 
                        PART I.  FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS
         --------------------


                         BARRETT RESOURCES CORPORATION
 
                     CONSOLIDATED CONDENSED BALANCE SHEETS
                                (in thousands)

<TABLE>
<CAPTION>
<S>                                              <C>          <C>
 
                                                  March 31,    December 31,
                                                    1998           1997
                                               ------------   ------------
ASSETS                                          (Unaudited)
Current assets:
 Cash and cash equivalents                         $ 12,055       $ 14,479
 Receivables, net                                    87,958        102,934
 Inventory                                            1,327          2,579
 Other current assets                                 1,199          1,701
                                               ------------   ------------
  Total current assets                              102,539        121,693
 
Property and equipment, net                         785,498        747,175
Other assets, net                                     3,727          3,833
                                               ------------   ------------
                                                   $891,764       $872,701
                                               ============   ============
 
LIABILITIES AND STOCKHOLDERS' EQUITY
 
Current liabilities:
 Accounts payable                                  $ 74,242       $ 61,870
 Amounts payable to oil and gas property
  owners                                             21,346         27,174
 Production taxes payable                            19,698         17,945
 Accrued and other liabilities                       14,071         17,917
                                               ------------   ------------
   Total current liabilities                        129,357        124,906
 
Long-term debt                                      262,018        266,437
 
Deferred income taxes                                72,635         68,977
 
Stockholders' equity:
 Preferred stock, $.001 par value:  1,000,000
  shares authorized, none outstanding                   --             --
 Common stock, $.01 par value:  45,000,000
  shares authorized; 31,682,395 issued
  (31,415,528 at December 31, 1997)                     317            314
 Additional paid-in capital                         256,546        247,390
 Retained earnings                                  170,891        164,677
                                               ------------   ------------
  Total stockholders' equity                        427,754        412,381
                                               ------------   ------------
                                                   $891,764       $872,701
                                               ============   ============
</TABLE>

                            See Accompanying Notes.

                                       3
<PAGE>
 
                         BARRETT RESOURCES CORPORATION

                  CONSOLIDATED CONDENSED STATEMENTS OF INCOME

                                  (UNAUDITED)
                     (in thousands, except per share data)


 
                                                  Three Months Ended
                                               ------------------------
                                                March 31,     March 31,
                                                  1998          1997
                                               ----------    ----------

 
Revenues:
  Oil and gas production                       $   54,227    $   53,035
  Trading revenues                                 74,857        22,267
  Revenue from gas gathering                          845           466
  Interest income                                     257           640
  Other income                                      1,533           144
                                               ----------    ----------
                                                  131,719        76,552
 
 
Operating expenses:
  Lease operating expenses                         15,674        16,477
  Cost of trading                                  69,945        21,820
  Depreciation, depletion and amortization         24,261        14,067
  General and administrative                        6,803         5,977
  Interest expense                                  4,709         2,223
  Other                                               305          ---
                                               ----------    ----------

                                                  121,697        60,564
                                               ----------    ----------
 
Income for the period before income taxes          10,022        15,988
Provision for income taxes                          3,808         6,075
                                               ----------    ----------
 

Net income for the period                      $    6,214    $    9,913
                                               ==========    ==========  


Earnings per common share
  Basic                                        $      .20    $      .32
                                               ==========    ==========
  Assuming dilution                            $      .19    $      .31
                                               ==========    ==========

                            See Accompanying Notes.

                                       4
<PAGE>
 
                      BARRETT RESOURCES CORPORATION
             CONSOLIDATED CONDENSED STATEMENTS OF CASH FLOWS
                                  (UNAUDITED)
                                (in thousands)
                                                       Three Months Ended
                                                    ------------------------
                                                     March 31,     March 31,
                                                       1998          1997
                                                    ----------    ----------
 
Cash flows from operations:
  Net income                                        $    6,214    $    9,913
  Adjustments needed to reconcile to
   net cash provided by operations:
    Depreciation, depletion, and amortization           24,362        14,117
    Deferred income taxes                                3,658         5,276
                                                    ----------    ----------
                                                        34,234        29,306
    Change in current assets and liabilities:
     Accounts receivable                                14,976        17,126
     Other current assets                                  502            65
     Accounts payable                                   12,372        (9,498)
     Amounts due oil and gas owners                     (5,828)        4,089
     Production taxes payable                            1,753         1,758
     Accrued and other liabilities                      (8,075)        1,211
                                                    ----------    ----------
Net cash flow provided by operations                    49,934        44,057
                                                    ----------    ----------
 
Cash flows from investing activities:
  Proceeds from sale of oil and gas properties           3,344          --
  Acquisition of property and equipment                (55,555)      (78,683)
                                                    ----------    ----------
Net cash flow used in investing activities             (52,211)      (78,683)
                                                    ----------    ----------
 
Cash flows from financing activities:
  Proceeds from issuance of common stock                    43           227
  Net payments under line of credit                        ---       (70,000)
  Proceeds from issuance of Senior Notes, net of
   offering costs                                          ---       146,009
  Payments on other long-term debt                        (190)          (70)
                                                    ----------    ----------
 
Net cash flow (used) provided by
 financing activities                                     (147)       76,166
                                                    ----------    ----------
 
(Decrease) increase in cash and
  cash equivalents                                      (2,424)       41,540
Cash and cash equivalents at beginning of period        14,479        14,539
                                                    ----------    ----------
 
Cash and cash equivalents at end of period          $   12,055    $   56,079
                                                    ==========    ==========
 
Non-cash investing and financing activities:
  Assumption of debt with property acquisition      $      ---    $    2,785
  Issuance of common stock for property
  acquisition                                       $    9,116    $      ---


                            See accompanying notes.

                                       5
<PAGE>
 
                         BARRETT RESOURCES CORPORATION
             NOTES TO CONSOLIDATED CONDENSED FINANCIAL STATEMENTS
                                March 31, 1998

1.   UNAUDITED CONSOLIDATED CONDENSED FINANCIAL STATEMENTS

     In the opinion of management, the accompanying unaudited consolidated
     condensed financial statements contain all adjustments necessary to present
     fairly the financial position of Barrett Resources Corporation and its
     wholly owned subsidiaries, collectively referred to as the "Company", as of
     March 31, 1998 and the results of operations and cash flows for the periods
     presented. All such adjustments are of a normal recurring nature. The
     results of operations for the periods presented are not necessarily
     indicative of the results for the full year.
 
     The accounting policies followed by the Company are set forth in Note 1 to
     the Company's financial statements in Form 10-K for the year ended December
     31, 1997. These financial statements should be read in conjunction with the
     financial statements and notes included in the Form 10-K.

2.   INCOME TAXES

     Provisions for income taxes were calculated in accordance with Statement of
     Financial Accounting Standards No. 109 which provides that a deferred tax
     liability or asset be determined based on the timing differences between
     the basis used for financial versus tax reporting of assets and liabilities
     as measured by the effective tax rates.  For the quarter ended March 31,
     1998, the Company  used an estimated effective tax rate of 38 percent.

     The Company is vigorously contesting a "Notice of Deficiency" of $5.3
     million together with penalties of $1.1 million, and an undetermined amount
     of interest, issued by the Internal Revenue Service resulting from an
     examination of federal tax returns of a subsidiary of the Company for years
     1991 through 1993. The deficiency resulted primarily from the IRS's
     disallowance of certain net operating loss deductions claimed during the
     periods under examination and may affect approximately $30 million of
     related net operating loss carryforwards. The Company believes that the
     federal returns of the subsidiary properly reflect the federal tax
     liability and that the existing net operating loss carryforwards are
     appropriate as supported by relevant authority. The trial of this matter
     began May 7, 1998. A decision is not expected until the first quarter of
     1999.

                                       6
<PAGE>
 
                         BARRETT RESOURCES CORPORATION
              NOTES TO CONSOLIDATED CONDENSED FINANCIAL STATEMENTS
                                 March 31, 1998

3.   LONG-TERM DEBT

     The Company's long-term debt consists of the following (in thousands):

                                    March 31,        December 31,
                                      1998               1997
                                  ------------       ------------
          Line of Credit            $100,000           $100,000
          7.55% Senior Notes         150,000            150,000
          Production Payments         17,041             17,231
                                    --------           --------
            Total                    267,041            267,231
          Less: current portion        5,023                794
                                    --------           --------
          Long-term debt            $262,018           $266,437
                                    ========           ========

     As of March 31, 1998 the Company's effective interest rate, on an
     outstanding balance of $100 million on its line of credit, was 6.074% per
     annum.

     Total interest expense paid for the quarter ended March 31, 1998 was $7.2
     million.

     On May 6, 1998, the Company filed a shelf registration statement with the
     Securities and Exchange Commission that would permit the issuance of up to
     $500 million in unsecured debt and/or equity securities, including common
     stock, preferred stock, warrants and depositary shares. Net proceeds, terms
     and pricing of any offerings of securities issued under the shelf
     registration statement will be determined at the time of the offering.
     There have been no securities issued, and no determination by the Company
     to issue any securities, under this shelf registration. Neither the filing
     nor the anticipated effectiveness of the shelf registration statement
     obligates the Company to issue any securities.
 
4.   EARNINGS PER SHARE

     The Company adopted Statement of Financial Accounting Standards No. 128,
     Earnings Per Share (SFAS No. 128) effective December 15, 1997. This
     pronouncement requires restatement of earnings per share for all prior
     periods presented.  As a result, the Company's reported earnings per share
     for the three months ended March 31, 1997 has been restated.

                                       7
<PAGE>
 
     The following data show the amounts used in computing earnings per share
     and the effect on income and the weighted average number of shares of
     dilutive potential common stock.

<TABLE>
<CAPTION>
     For the three months ended March 31,
      (in thousands)                                                  1998           1997
                                                                    ---------     ---------
<S>                                                                 <C>           <C>
Income available to common stockholders                             $   6,214     $   9,913
                                                                    =========     =========
Weighted average number of common shares used in   
 basic EPS                                                             31,418        31,339
Effect of dilutive securities:
  Stock options                                                           354           605
  Written put option                                                      150           --
                                                                    ---------     ---------
Weighted number of common shares and dilutive
  potential common stock used in EPS               
  assuming dilution                                                    31,922        31,914
                                                                    =========     =========
</TABLE>
                                                                                
5.   ACQUISITION

     On March 31, 1998, the Company issued 260,917 shares of its common stock to
     acquire Advantage Resources International, Inc.-Peru, whose sole asset is a
     15 percent interest in an oil and gas license covering an area denominated
     as Block 67 located in the Republic of Peru. This transaction was accounted
     for as a purchase.
 

 

                                       8
<PAGE>
 
                         BARRETT RESOURCES CORPORATION
                             For the Quarter Ended
                                March 31, 1998


Item 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
         ---------------------------------------------------------------
         RESULTS OF OPERATIONS
         ---------------------


Liquidity and Capital Resources
-------------------------------

     For the three months ended March 31, 1998, total assets increased $19.1
     million, or two percent, to $891.8 million as compared with total assets of
     $872.7 million at December 31, 1997. Cash and cash equivalents decreased
     $2.4 million to $12.1 million, working capital decreased to a negative
     $26.8 million, and property and equipment increased $38.3 million to $785.5
     million.

     Operating cash flows before working capital adjustments totaled $34.2
     million in the first quarter of 1998 compared with $29.3 million in the
     first quarter of 1997. After working capital adjustments, cash flow
     provided by operations increased by $5.9 million to $49.9 million as
     compared with the same period in 1997.

     On May 6, 1998, the Company filed a shelf registration statement with the
     Securities and Exchange Commission that would permit the issuance of up to
     $500 million in unsecured debt and/or equity securities, including common
     stock, preferred stock, warrants and depositary shares.  Net proceeds,
     terms and pricing of offerings of securities issued under the shelf
     registration statement will be determined at the time of the offering.
     There have been no securities issued, and no determination by the Company
     to issue any securities, under this shelf registration. Neither the filing
     nor the anticipated effectiveness of the shelf registration statement
     obligates the Company to issue any securities.

     On March 31, 1998, the Company issued 260,917 shares of common stock in an
     acquisition of a company whose sole asset is a 15 percent interest in an
     oil and gas license covering an area denominated as Block 67 located in the
     Republic of Peru. The Company has a 70 percent interest in Block 67.

     Capital expenditures of $64.7 million for the quarter represent a decrease
     of $16.8 million from the same period in 1997. These expenditures, funded
     by operating cash flows and issuance of the Company's common stock,
     consisted principally of drilling and development activities and
     acquisitions of oil and gas properties. Of these capital expenditures,
     approximately 53 percent was invested in the Rocky Mountain Region,
     principally in the Piceance, Powder River and Wind River Basins, 13 percent
     in the Mid-Continent Region, 25 percent in the Gulf Coast Region and 15
     percent in international activities in the Republic of Peru.

                                       9
<PAGE>
 
     The Company plans to continue actively acquiring, exploring and developing
     oil and gas properties.  The Company expects cash flow from its producing
     properties and its borrowing capacity to be sufficient to fund its
     anticipated capital and operating requirements, including any
     contingencies.

     The Company is evaluating its information technology infrastructure for
     Year 2000 compliance. The Company does not expect that the cost, if any, to
     modify its information technology infrastructure to become Year 2000
     compliant will be material to its financial condition or results of
     operations. The Company does not anticipate any material disruption in its
     operations as a result of any failure by the Company, its customers or
     suppliers to be in compliance.

     The Company's operating results are directly affected by oil and gas
     prices.  Oil and gas prices also affect the reserve values used in
     determining the "ceiling test" limitation for the Company's capitalized oil
     and gas property costs accounted for under the full cost method. Should the
     net capitalized costs of the Company's oil and gas properties exceed the
     estimated present value of future net cash flows from proved oil and gas
     reserves, such excess costs would be recognized as an impairment and
     charged to current expense. A decline in oil and gas sales prices could
     possibly result in the recognition of an impairment expense in future
     periods.

Results of Operations
---------------------

     Net income for the quarters ended March 31, 1998 and 1997 was $6.2 million
     ($.19 per share, assuming dilution) and $9.9 million ($.31 per share,
     assuming dilution), respectively.  This decrease is primarily due to lower
     prices for oil and gas, and to increased depreciation, depletion and 
     amortization and interest expense.

     Total revenues for the quarter were $131.7 million, up 72 percent compared
     to $76.6 million for the same period in 1997.  This increase is principally
     attributed to a $52.6 million increase in trading revenues.

     Production revenue for the first quarter of 1998 increased 2.2 percent from
     $53.0 million to $54.2 million.  Production revenues and related volumes
     and average prices during the periods presented were as follows:

                                              Quarter Ended
                                                March 31,
                                          ---------------------
                                           1998           1997
                                          -------       -------
     Gas Revenues (000's)                 $45,620       $42,928
     Gas Production (Bcf)                    22.9          17.3
     Average Price per Mcf                $  1.99       $  2.49
 
     Oil Revenues (000's)                 $ 8,607       $10,107
     Oil Production (MBbls)                   648           501
     Average Price per Barrel             $ 13.28       $ 20.17

     (Note: Bcf = billion cubic feet;  Mcf = thousand cubic feet; MBbls =
     thousand barrels.)

                                       10
<PAGE>
 
     First quarter gas revenues increased 6.3 percent as compared with the same
     period in 1997, principally due to a 32.4 percent increase in production
     volumes.

     The 14.8 percent decrease in first quarter 1998 oil revenues from the same
     period in 1997 is attributed to a 34.2 percent decrease in average oil
     prices partially offset by a 29.3 percent increase in production volumes.

     For the quarter ended March 31, 1998, revenues from trading were $74.9
     million compared to $22.3 million for the same period in 1997.  The
     associated costs of trading increased to $69.9 million from $21.8 million.
     Gross profit from trading was $4.9 million and $447,000 for the respective
     quarters ended March 31, 1998 and 1997.

     To reduce its exposure to volatile gas prices fluctuations, the Company
     enters into hedging arrangements for both trading and producing activities.
     During the first quarter ended March 31, 1998, the Company recognized net
     producing hedging expenses of approximately $335,000 which was recorded in
     the consolidated statements of income as adjustments to gas production
     revenue.  The Company realized net hedging income on its trading activities
     of approximately $2.7 million.

     Production costs decreased in the first quarter of 1998 compared with the
     same period in 1997 primarily as a result of an improvement to the high
     operating costs of oil properties located in the Uinta Basin of Utah. In
     1997, the Company experienced additional start-up cost associated with
     restoring and/or improving the productive capabilities of these wells.

     Depreciation, depletion and amortization increased to $24.3 million from
     $14.1 million due to both a 32.1 percent increase in oil and gas equivalent
     production and an increase of the depletion rate from $.65 to $.87 per
     Mcfe.

     Interest expense for the first quarter increased from $2.2 million in 1997
     to $4.7 million in 1998 due to higher debt levels for the first quarter of
     1998 compared with the same period in 1997.

     The Company's largest source of operating income is from sales of its gas
     and oil production.  Therefore, the levels of the Company's revenues and
     earnings are affected by prices at which natural gas and oil are being
     sold.  This is particularly true with respect to natural gas, which
     accounted for approximately 84.1 percent of the Company's production
     revenue for the first quarter of 1998.  As a result, the Company's
     operating results for any prior period are not necessarily indicative of
     future operating results because of the fluctuations in gas and oil prices
     and the lack of predictability of those fluctuations as well as changes in
     production levels.

     _______________________________________________________________________

                                       11
<PAGE>
 
     This report contains forward-looking statements within the meaning of
     Section 27A of the Securities Act of 1933 and Section 21E of the Exchange
     Act of 1934. Although the Company believes that the expectations reflected
     in the forward-looking statements and the assumptions upon which such
     forward-looking statements are based are reasonable, it can give no
     assurance that such expectations and assumptions will prove to have been
     correct. See the Company's Annual Report on Form 10-K for additional
     statements concerning important factors that could cause actual results to
     differ materially from the Company's expectations.

                                       12
<PAGE>
 
                                 PART II.  OTHER INFORMATION

Item 1.   Legal Proceedings
          -----------------

          On April 3, 1998, Paul M. Rady filed a lawsuit against the Company in
          the District Court in and for Tulsa County, State of Oklahoma. Mr.
          Rady was the Chief Executive Officer and President of the Company
          until March 23, 1998, at which time the Company's Board of Directors
          replaced Mr. Rady in these positions. Mr. Rady also was a director and
          employee of the Company until April 30, 1998. In his complaint, Mr.
          Rady makes various allegations and claims concerning the Company and
          Mr. Rady's employment. Mr. Rady claims damages in excess of $10,000 on
          each of his three causes of action, which he requests be determined at
          a trial, as well as punitive and exemplary damages. The Company
          believes that Mr. Rady's claims are without merit.

          For information regarding certain other legal proceedings, reference
          is made to the Company's Form 10-K for the year ended December 31,
          1997, which is incorporated by reference, and to Note 2 in Part I of
          this Form 10-Q Report.

Item 6.   Exhibits and Reports on Form 8-K
          --------------------------------

          (a)  The following Exhibit is filed as part of this Quarterly Report
               on Form 10-Q:

               27.1  Financial Data Schedule
               27.2  Financial Data Schedule Restated for quarters ending 
                     March 31, June 30 and September 30, 1997
               27.3  Financial Data Schedule Restated for quarter ended June 30,
                     1996 and for the twelve month period ended December 31,
                     1996

          (b)  During the quarter ended March 31, 1998, the Registrant filed one
               report on Form 8-K reporting events occurring on March 23, 1998.

                                       13
<PAGE>
 
                                 SIGNATURES
                                 ----------


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

                                       BARRETT RESOURCES CORPORATION


May 11, 1998                           By /s/ A. Ralph Reed
                                          -----------------
                                          A. Ralph Reed
                                          President and
                                              Chief Operating Officer


May 11, 1998                           By /s/ J. Frank Keller
                                          --------------------
                                          J. Frank Keller
                                          Chief Financial Officer

                                       14