<PAGE>   1
 
================================================================================
 
                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, 1997
 
                                       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)
 
<TABLE>
<C>                                            <C>
                   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)
</TABLE>
 
                                 (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 31,341,776 shares of the registrant's $.01 par value
                  common stock outstanding as of May 9, 1997.
 
================================================================================
<PAGE>   2
 
                         BARRETT RESOURCES CORPORATION
 
                                     INDEX
 
<TABLE>
<CAPTION>
                                                                         PAGE
                                                                         ----
<S>        <C>                                                           <C>
PART I. FINANCIAL INFORMATION
  Item 1.  Financial Statements
           Consolidated Condensed Balance Sheets -- March 31, 1997 and
             December 31, 1996.........................................    3
           Consolidated Condensed Statements of Income -- Three Months
             Ended March 31, 1997 and 1996.............................    4
           Consolidated Condensed Statements of Cash Flows -- Three
             Months Ended March 31, 1997 and 1996......................    5
  Item 2.  Management's Discussion and Analysis of Financial Condition
             and Results of Operations.................................    8
PART II. OTHER INFORMATION
  Item 6.  Exhibits and Reports on Form 8-K............................   10
</TABLE>
 
                                        2
<PAGE>   3
 
                         PART I. FINANCIAL INFORMATION
 
ITEM 1. FINANCIAL STATEMENTS
 
                         BARRETT RESOURCES CORPORATION
 
                     CONSOLIDATED CONDENSED BALANCE SHEETS
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                               MARCH 31,    DECEMBER 31,
                                                                 1997           1996
                                                              -----------   ------------
                                                              (UNAUDITED)
<S>                                                           <C>           <C>
ASSETS
Current assets:
  Cash and cash equivalents.................................   $ 56,079       $ 14,539
  Receivables, net..........................................     55,919         73,045
  Inventory.................................................      4,520            947
  Other current assets......................................      1,091          1,156
                                                               --------       --------
          Total current assets..............................    117,609         89,687
Property and equipment, net.................................    551,086        487,258
Debt issue costs, net of amortization.......................      3,941             --
                                                               --------       --------
                                                               $672,636       $576,945
                                                               ========       ========
LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
  Accounts payable..........................................   $ 32,119       $ 41,617
  Amounts payable to oil and gas property owners............     22,585         18,496
  Production taxes payable..................................     15,588         13,830
  Accrued and other liabilities.............................      6,370          4,374
                                                               --------       --------
          Total current liabilities.........................     76,662         78,317
Long-term debt..............................................    151,930         70,000
Deferred income taxes.......................................     56,184         50,908
Stockholders' equity:
  Preferred stock, $.001 par value: 1,000,000 shares
     authorized, none outstanding...........................         --             --
  Common stock, $.01 par value: 35,000,000 shares
     authorized; 31,340,876 issued (31,330,361 at December
     31, 1996)..............................................        314            313
  Additional paid-in capital................................    242,217        241,991
  Retained earnings.........................................    145,329        135,416
                                                               --------       --------
          Total stockholders' equity........................    387,860        377,720
                                                               --------       --------
                                                               $672,636       $576,945
                                                               ========       ========
</TABLE>
 
                            See accompanying notes.
 
                                        3
<PAGE>   4
 
                         BARRETT RESOURCES CORPORATION
 
                  CONSOLIDATED CONDENSED STATEMENTS OF INCOME
                                  (UNAUDITED)
                     (IN THOUSANDS, EXCEPT PER SHARE DATA)
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED
                                                              ----------------------
                                                              MARCH 31,    MARCH 31,
                                                                1997         1996
                                                              ---------    ---------
<S>                                                           <C>          <C>
Revenues:
  Oil and gas production....................................   $53,035      $29,544
  Trading revenues..........................................    22,267       11,993
  Revenue from gas gathering................................       466          448
  Interest income...........................................       640          197
  Other income..............................................       144          125
                                                               -------      -------
                                                                76,552       42,307
Operating expenses:
  Lease operating expenses..................................    16,477       10,947
  Cost of trading...........................................    21,820       11,214
  Depreciation, depletion and amortization..................    14,067        9,404
  General and administrative................................     5,977        3,618
  Interest expense..........................................     2,223        1,551
                                                               -------      -------
                                                                60,564       36,734
                                                               -------      -------
Income for the period before income taxes...................    15,988        5,573
Provision for income taxes..................................     6,075        2,117
                                                               -------      -------
Net income for the period...................................   $ 9,913      $ 3,456
                                                               =======      =======
Net income per common share and common share equivalent.....   $   .31      $   .14
                                                               =======      =======
Weighted average number of shares of common stock and common
  stock equivalents.........................................    31,945       25,234
                                                               =======      =======
</TABLE>
 
                            See accompanying notes.
 
                                        4
<PAGE>   5
 
                         BARRETT RESOURCES CORPORATION
 
                CONSOLIDATED CONDENSED STATEMENTS OF CASH FLOWS
                                  (UNAUDITED)
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED
                                                              ----------------------
                                                              MARCH 31,    MARCH 31,
                                                                1997         1996
                                                              ---------    ---------
<S>                                                           <C>          <C>
Cash flows from operations:
  Net income................................................  $  9,913     $  3,456
  Adjustments needed to reconcile to net cash provided by
     operations:
     Depreciation, depletion, and amortization..............    14,117        9,404
     Amortization of unrealized hedging (losses)............        --       (1,138)
     Deferred income taxes..................................     5,276        1,838
                                                              --------     --------
                                                                29,306       13,560
  Change in current assets and liabilities:
     Accounts receivable....................................    17,126       (4,856)
     Other current assets...................................        65          (65)
     Accounts payable.......................................    (9,498)         119
     Amounts due oil and gas owners.........................     4,089          782
     Production taxes payable...............................     1,758        4,035
     Accrued and other liabilities..........................     1,211         (350)
                                                              --------     --------
Net cash flow provided by operations........................    44,057       13,225
                                                              --------     --------
Cash flows from investing activities:
  Proceeds from sale of oil and gas properties..............        --          135
  Acquisition of property and equipment.....................   (78,683)     (22,173)
                                                              --------     --------
Net cash flow used in investing activities..................   (78,683)     (22,038)
                                                              --------     --------
Cash flows from financing activities:
  Proceeds from issuance of common stock....................       227        1,229
  Net (payments) borrowings under line of credit............   (70,000)      11,000
  Proceeds from issuance of Senior Notes, net of offering
     costs..................................................   146,009           --
  Payments on other long-term debt..........................       (70)          --
                                                              --------     --------
Net cash flow provided by financing activities..............    76,166       12,229
                                                              --------     --------
Increase in cash and cash equivalents.......................    41,540        3,416
Cash and cash equivalents at beginning of period............    14,539        7,529
                                                              --------     --------
Cash and cash equivalents at end of period..................  $ 56,079     $ 10,945
                                                              ========     ========
Non-cash investing and financing activities:
  Assumption of debt with property acquisition..............  $  2,785           --
</TABLE>
 
                            See accompanying notes.
 
                                        5
<PAGE>   6
 
                         BARRETT RESOURCES CORPORATION
 
              NOTES TO CONSOLIDATED CONDENSED FINANCIAL STATEMENTS
                                 MARCH 31, 1997
 
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,
1997 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,
1996. These financial statements should be read in conjunction with the
financial statements and notes included in the Form 10-K. Certain
reclassifications have been made to 1996 amounts to conform to the 1997
presentation.
 
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, 1997, the
Company used an estimated effective tax rate of 38 percent. Approximately
$250,000 of income taxes was paid in the first quarter ended March 31, 1997.
 
     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 unused 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. It is
anticipated that the final determination of this matter will involve a lengthy
process.
 
3. LONG-TERM DEBT
 
     The Company's long-term debt consists of the following (in thousands):
 
<TABLE>
<CAPTION>
                                                              MARCH 31,    DECEMBER 31,
                                                                1997           1996
                                                              ---------    ------------
<S>                                                           <C>          <C>
7.55% Senior Notes..........................................  $150,000       $    --
Credit facility.............................................        --        70,000
Other.......................................................     2,715            --
                                                              --------       -------
                                                               152,715        70,000
Less current portion........................................       785            --
                                                              --------       -------
                                                              $151,930       $70,000
                                                              ========       =======
</TABLE>
 
     In February 1997, the Company issued $150 million principal amount of 7.55%
Senior Notes due 2007 ("Notes"). A portion of the net proceeds from the offering
was used to repay in full the balance of the
 
                                        6
<PAGE>   7
 
Company's existing line of credit. Interest on the Notes is payable
semi-annually on February 1 and August 1 of each year, commencing August 1,
1997.
 
     Total interest expense paid for the quarter ended March 31, 1997 was
$677,000.
 
4. SUBSEQUENT EVENT
 
     In April 1997, the Company acquired additional interests in certain
properties located in the Piceance Basin of Colorado from an industry partner.
This transaction involved the formation of a Colorado limited liability
corporation ("LLC") in which both entities contributed properties located in the
Piceance Basin with the Company being the managing member of the LLC. The
Company's partner in the LLC may require, at any time prior to February 1, 2012,
the Company to purchase its interest in the LLC. Conversely, the Company may
require, at any time after January 1, 2002 but prior to January 31, 2012, this
partner to sell its interest in the LLC to the Company. Should either of these
options be exercised, the Company will issue 150,000 shares of its Common Stock
as payment for the LLC interest.
 
5. RECENTLY ISSUED ACCOUNTING STANDARD
 
     In February 1997, the Financial Accounting Standards Board issued Statement
of Financial Accounting Standards ("SFAS") No. 128 "Earnings per Share." The
purpose of SFAS No. 128 is to simplify the computation of earnings per share
("EPS") and to make the U.S. standard for computing EPS more compatible with the
EPS standards of other countries and with that of the International Accounting
Standards Committee. The effective date for the application of SFAS No. 128 for
both interim and annual periods is after December 15, 1997. Earlier application
is not permitted. The Company does not expect the application of SFAS No. 128 to
have a material impact on its EPS calculation.
 
                                        7
<PAGE>   8
 
                         BARRETT RESOURCES CORPORATION
 
                             FOR THE QUARTER ENDED
                                 MARCH 31, 1997
 
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, 1997, total assets increased $95.7
million, or 16 percent, to $672.6 million as compared with total assets of
$576.9 million at December 31, 1996. Cash and short term investments increased
$41.5 million to $56.1 million, working capital increased $29.6 million to $40.9
million and property and equipment increased $63.8 million to $551.1 million.
During the quarter, the Company actively invested in oil and gas properties in
its areas of activity, which increased both property and equipment and long-term
debt.
 
     In February 1997, the Company issued $150 million principal amount of 7.55%
Senior Notes due 2007 ("Notes"). A portion of the net proceeds from the offering
was used to repay in full the $85 million outstanding balance of the Company's
existing line of credit. At the end of the quarter, total long-term debt was
$151.9 million, an increase of $81.9 million from year-end 1996. This increase
results primarily from the issuance of the Notes which exceeded the Company's
long-term debt at that time. Management anticipates that the remainder of the
proceeds from the Notes will be utilized for drilling, development and leasehold
acquisition during 1997.
 
     Operating cash flows before working capital adjustments totaled $29.3
million in the first quarter of 1997 compared with $13.6 million in the first
quarter of 1996. After working capital adjustments, cash flow provided by
operations increased by $30.8 million to $44.1 million as compared with the same
period in 1996.
 
     Capital expenditures of $81.5 million for the quarter increased $59.3
million over the same period in 1996. These expenditures, funded by operating
cash flows and borrowings, consisted principally of drilling and development
activities of oil and gas properties. Of these capital expenditures,
approximately 30 percent was invested in the Rocky Mountain Region, principally
in the Piceance and Wind River Basins, 25 percent in the Mid-Continent Region
and 36 percent in the Gulf Coast Region.
 
     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. Sales prices of
the Company's oil and gas production declined significantly after December 31,
1996, but recovered slightly subsequent to March 31, 1997. A further 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, 1997 and 1996 was $9.9 million
($.31 per share) and $3.5 million ($.14 per share), respectively. This increase
is primarily due to increased oil and gas production revenue which resulted from
both higher production volumes and from increased average oil and gas sales
prices for the quarter.
 
                                        8
<PAGE>   9
 
     Total revenues for the quarter were $76.6 million, up 81 percent compared
to $42.3 million for the same period in 1996. This increase is attributed to
higher production revenues and a $10.3 million increase in trading revenues.
 
     Production revenue for the first quarter of 1997 increased 80 percent from
$29.5 million to $53.0 million. Production revenues and related volumes and
average prices during the periods presented were as follows:
 
<TABLE>
<CAPTION>
                                                             QUARTER ENDED
                                                               MARCH 31,
                                                          --------------------
                                                           1997         1996
                                                          -------      -------
<S>                                                       <C>          <C>
Gas Revenues (000's)....................................  $42,928      $22,444
Gas Production (Bcf)....................................     17.3         13.5
Average Price per Mcf...................................  $  2.49      $  1.67
Oil Revenues (000's)....................................  $10,107      $ 7,100
Oil Production (MBbls)..................................      501          430
Average Price per Barrel................................  $ 20.17      $ 16.51
</TABLE>
 
---------------
 
        (Note: Bcf = billion cubic feet; Mcf = thousand cubic feet; MBbls =
thousand barrels)
 
     First quarter gas revenues increased 91 percent as compared with the same
period in 1996, principally due to a 28 percent increase in production volumes
and a 49 percent increase in average gas prices.
 
     The 42 percent increase in first quarter 1997 oil revenues from the same
period in 1996 is directly attributed to a 22 percent increase in average oil
prices and a 17 percent increase in production volumes.
 
     For the quarter ended March 31, 1997, revenues from trading were $22.3
million compared to $12.0 million for the same period in 1996. The associated
costs of trading increased to $21.8 million from $11.2 million. Gross profit
from trading was $447,000 and $779,000 for the respective quarters ended March
31, 1997 and 1996.
 
     To reduce its exposure to volatile oil and gas price fluctuations, the
Company enters into hedging arrangements for both trading and producing
activities. During the first quarter ended March 31, 1997, the Company
recognized net producing hedging expenses of $3.5 million which was recorded in
the consolidated statements of income as adjustments of oil and gas production
revenue. As of March 31, 1997, the Company held positions to hedge 1997 gas
production of 20,000 MMBtu per day for April through October and an additional
10,000 MMBtu per day for May through July.
 
     Production costs increased due primarily to an increase in the number of
producing wells and higher operating costs for the Uinta Basin properties.
During 1996, the Company increased its producing well count by 111 net gas wells
and 69 net oil wells, most of which were added subsequent to the first quarter
of 1996. The Company experienced additional production costs during the first
quarter of 1997 on oil properties located in the Uinta Basin which were acquired
in the fourth quarter of 1996. These additional costs were associated with
restoring and/or improving the productive capabilities of these wells. The Uinta
Basin's lease operating expenses (LOE) were 34% of the Company's total LOE for
the 1997 quarter. It is anticipated that the majority of these costs are
one-time start-up costs.
 
     Depreciation, depletion and amortization increased to $14.1 million from
$9.4 million due to a 26 percent increase in oil and gas equivalent production.
During the 1997 and 1996 quarters, depletion on oil and gas production was
recorded at $3.90 and $3.36 per BOE, respectively.
 
     Interest expense for the first quarter increased from $1.6 million in 1996
to $2.2 million in 1997 due to higher debt levels for the first quarter in 1997
compared with same period in 1996. This expense was partially
 
                                        9
<PAGE>   10
 
offset by higher interest income generated from short-term investments of
available funds principally provided by the issuance of the Senior Notes
described in "Liquidity and Capital Resources" above.
 
     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
81 percent of the Company's production revenue for the first quarter of 1997. 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.
 
     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.
 
                           PART II. OTHER INFORMATION
 
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. Financial Data Schedule
 
     (b) During the quarter ended March 31, 1997, the Registrant filed three
         reports on Form 8-K reporting events occurring on each of January 8,
         1997, February 7, 1997 and February 13, 1997, respectively.
 
                                       10
<PAGE>   11
 
                                   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 13, 1997                                By        /s/ PAUL M. RADY
                                             -----------------------------------
                                                        PAUL M. RADY
                                                          PRESIDENT
 
May 13, 1997                                By      /s/ J. FRANK KELLER
                                             -----------------------------------
                                                       J. FRANK KELLER
                                                   CHIEF FINANCIAL OFFICER
 
                                       11
<PAGE>   12
                                 EXHIBIT INDEX

<TABLE>
<CAPTION>
EXHIBIT NO.             DESCRIPTION
-----------             -----------
<S>             <C>

   27           FINANCIAL DATA SCHEDULE
</TABLE>