<PAGE>
 
                      SECURITIES AND EXCHANGE COMMISSION

                            Washington, D. C. 20549

                                   Form 10-Q

               QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15 (D)
                    OF THE SECURITIES EXCHANGE ACT OF 1934


For the Quarter ended
   March 31, 1998                               Commission File Number 2-71865
---------------------                           ------------------------------ 


                      TEXLAND DRILLING PROGRAM-1981, LTD.
                      -----------------------------------
                             (Name of Registrant)


      TEXAS                                             75-1791491              
-------------------                        ------------------------------------ 
(State of Organization)                    (I.R.S. Employer Identification No.) 


500 Throckmorton Street, Suite 3100
        Fort Worth, Texas                                            76102  
-----------------------------------                                 --------
 (Address of Executive Offices)                                     Zip Code 


                Registrant's Telephone Number   (817) 336-2751
                                                --------------

          Securities registered pursuant to Section 12(b) of the Act:

Units of Limited Partnership Interest                                None 
-------------------------------------                           -------------
     (Title of Class)                                           (Voting Units)



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 
        ---      ---


                   This report contains a total of 10 pages.

                                       1
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                                        
                         INDEX TO FINANCIAL STATEMENTS
                                        

                                 Reference Page
                                 --------------

Balance Sheets at March 31, 1998 and                            3
    December 31, 1997.
 
Statements of Operations for the Three Months                   4
    Ended March 31, 1998 and 1997.
 
Statement of Partners' Equity at March 31, 1998.                5
 
Statements of Cash Flows for Three Months Ended                 6
    March 31, 1998 and 1997.
 
Notes to Financial Statements.                                7-8

                                       2
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A LIMITED PARTNERSHIP)

                                BALANCE SHEETS
                     March 31, 1998 and December 31, 1997
                                  (Unaudited)

ASSETS
                                                   3/31/98       12/31/97
                                                 -----------    -----------
CURRENT ASSETS                                   
  Cash                                           $    62,551    $    63,132
  Accounts Receivable
     Trade                                            79,055        117,054
     General Partner                                       -              -
                                                 -----------    -----------
     Total Current Assets                            141,606        180,186

PROPERTY AND EQUIPMENT, AT COST
  (SUCCESSFUL EFFORTS METHOD)
  Intangible Development Costs                     7,856,987      7,856,343
  Lease and Well Equipment                         4,567,753      4,562,176
  Producing Leaseholds                               373,207        373,188
                                                 -----------    -----------
                                                  12,797,947     12,791,718
  Less: Accumulated Depreciation, Depletion
     & Amortization                                9,923,960      9,845,056
                                                 -----------    -----------
                                                   2,873,987      2,946,662
  Wells-in-Progress
  Nonproducing Leaseholds                                  -              -
                                                 -----------    -----------
     Net Property, Plant and Equipment             2,873,987      2,946,662

Organizational Costs (net of $1,141,028
  amortization in 1991 and $1,069,798
  in 1990)                                                 -              -
                                                 -----------    -----------
  Total Assets                                   $ 3,015,593    $ 3,126,848
                                                 ===========    ===========

LIABILITIES AND PARTNERS' EQUITY

CURRENT LIABILITIES
  Accounts Payable - Trade                            43,737         49,218
                                                 -----------    -----------
  Total Current Liabilities                           43,737         49,218

PARTNERS' EQUITY
  Limited Partners - 2,425 Units Outstanding       2,158,262      2,232,831
  General Partner                                    813,594        844,799
                                                 -----------    -----------
  Total Partners' Equity                           2,971,856      3,077,630
                                                 -----------    -----------
  Total Liabilities and Partners' Equity           3,015,593      3,126,848
                                                 ===========    ===========


                            See Accompanying Notes

                                       3



<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A LIMITED PARTNERSHIP)

                            STATEMENT OF OPERATIONS
                            March 31, 1998 and 1997
                                  (Unaudited)


<TABLE> 
<CAPTION> 
                                                             Three Months Ended       
                                                                   March 31,          
                                                                 1998        1997     
                                                           ----------  ----------     
<S>                                                        <C>         <C>            
REVENUES                                                                              
 Oil and Gas Sales                                         $  265,746  $  441,758     
 Interest Income                                                  439         893     
 Gain on Sale                                                       -           -     
                                                           ----------  ----------     
                                                              266,185     442,651     
                                                                                      
EXPENSES                                                                              
 Fees to Managing General Partner                              24,260      16,050     
 Production Expenses                                          123,326     112,264     
 Severance Tax Withholding                                     12,224      21,859     
 Depreciation, Depletion & Amortization Expenses               78,905      89,066     
 Other Expenses                                                 1,691      (6,947)    
                                                           ----------  ----------     
                                                              240,406     232,292     
                                                           ----------  ----------     
NET INCOME (LOSS)                                          $   25,779  $  210,359     
                                                           ----------  ----------     
                                                                                      
NET INCOME (LOSS) ALLOCATION                                                          
 Limited Partners                                               5,636     105,336     
 General Partner                                               20,144     105,024     
                                                           ----------  ----------     
                                                           $   25,779  $  210,359     
                                                           ----------  ----------     
NET INCOME (LOSS) PER $5,000 LIMITED PARTNER UNIT                                     
 (2,425 UNITS OUTSTANDING)                                 $        2  $       43     
                                                           ----------  ----------     
</TABLE> 

                            See Accompanying Notes

                                       4
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A LIMITED PARTNERSHIP)

                         STATEMENT OF PARTNERS' EQUITY
                       Three Months Ended March 31, 1998
                                  (Unaudited)


                                                        Limited        General
                                          Total         Partner        Partner
                                        ----------     ----------     ----------

BALANCE DECEMBER 31, 1997               $3,077,630     $2,225,376      $852,254

Partners' Contributions                      5,596                        5,596

Partners' Distributions                   (137,150)       (72,750)      (64,400)

Net Income (Loss)                           25,779          5,636        20,144
                                        ----------     ----------     ----------
BALANCE MARCH 31, 1998                  $2,971,856     $2,158,262      $813,594
                                        ==========     ==========     ==========

                            See Accompanying Notes

                                       5
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A LIMITED PARTNERSHIP)

                            STATEMENTS OF CASH FLOW
                  Three Months Ended March 31, 1998 and 1997
                                  (Unaudited)


<TABLE> 
<CAPTION> 
                                                                            1998              1997
                                                                        --------          --------
<S>                                                                     <C>               <C> 
CASH FLOWS FROM OPERATING ACTIVITIES                                    $ 25,779          $154,767
 Net Income (Loss)
 Adjustments to Reconcile Net Income to Net Cash Provided by
    Operating Activities:
    Depreciation, Depletion and Amortization Expenses                     78,905            75,581
    Abandoned Leaseholds
    Loss on Sale of Assets
    Change in Accounts Receivable                                         37,999            58,764
    Change in Accounts Payable                                            (5,481)           12,468
                                                                        --------          --------
    Total Adjustments                                                    111,423           146,813
                                                                        --------          --------
    Net Cash Provided by Operating Activities                            137,202           301,580

CASH FLOWS FROM INVESTING ACTIVITIES
 Acquisition of Property and Equipment                                    (6,229)          (99,118)
 Proceeds from Sale of Property and Equipment                                  -
                                                                        --------          --------
    Net Cash Used by Investing Activities                                 (6,229)          (99,118)

CASH FLOWS FROM FINANCING ACTIVITIES
 Partners' Contributions                                                   5,596            41,629
 Partners' Distributions                                                (137,150)         (272,625)
                                                                        --------          --------
    Net Cash Used by Financing Activities                               (131,554)         (230,996)

NET INCREASE IN CASH                                                        (581)          (28,534)
Cash at Beginning of Year                                                 63,132            92,858
                                                                        --------          --------
CASH AT END OF QUARTER                                                  $ 62,551          $ 64,324
                                                                        ========          ========
</TABLE> 
              
                            See Accompanying Notes

                                       6
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A Limited Partnership)
                                        
                         NOTES TO FINANCIAL STATEMENTS
                                March 31, 1998
                                  (Unaudited)


1.  SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

The Partnership was organized as a limited partnership on June 20, 1981 for the
purpose of engaging in oil and gas exploration and production.  Texland
Properties-1981, a general partnership, and Texland Petroleum, Inc. are the
General Partners.  The Managing General Partner is Texland Petroleum, Inc.  The
Partnership's accounting policies are summarized below:

BASIS OF ACCOUNTING

The Partnership follows generally accepted accounting principles applicable to
established enterprises in the extractive industries under a method which is
generally known as the successful method of accounting.

PROPERTY AND EQUIPMENT

Costs incurred for the acquisition of producing and nonproducing leaseholds are
capitalized.  Costs of intangible development and lease and well equipment
incurred to drill and equip successful exploratory and development wells are
capitalized.  Costs to drill and equip unsuccessful exploratory wells are
charged to operations while costs of unsuccessful development wells remain
capitalized.  Costs associated with uncompleted wells are capitalized as wells-
in-progress.

ABANDONED LEASEHOLDS

Costs of nonproducing properties are charged to expense at such time as they are
deemed to be impaired, based upon periodic assessments of such costs.

DEPLETION

Leasehold costs of producing properties are amortized on the unit of production
method based on proved oil and gas reserves.  Intangible development costs of
producing properties are amortized on the unit of production method based on
estimated proved developed oil and gas reserves.

DEPRECIATION

Depreciation of equipment is provided by using the unit of production method
based on estimated proved developed oil and gas reserves.

ORGANIZATION COSTS

These costs are amortized by the straight-line method over ten years, the life
of the Partnership.

FEDERAL INCOME TAX

The Partnership files its federal income tax return on the accrual basis.

                                       7
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A Limited Partnership)
                                        
                   NOTES TO FINANCIAL STATEMENTS (CONTINUED)
                                March 31, 1998
                                  (Unaudited)


2.  CONTRIBUTIONS BY GENERAL PARTNER (TEXLAND PROPERTIES-1981)

Under terms of the Partnership Agreement, the General Partner is charged for
certain costs related to drilling and production operations which are required
to be capitalized for federal income tax purposes.  These costs are treated as
capital contributions by the General Partner.  In addition, Texland Properties-
1981 and Texland Petroleum, Inc. have invested in limited partnership units in
the amount of $95,000 and $30,000 respectively.

3.  FEES TO MANAGING GENERAL PARTNER (TEXLAND PETROLEUM, INC.)

In consideration of its management services rendered, the Managing General
Partner is entitled to charge management fees to the Partnership.  In addition,
for the three months ended March 31, 1998  and March 31, 1997, the Partnership
was charged $46,298 and $36,812 respectively for technical services, accounting
services, and supervisory services performed by the employees of the Managing
General Partner and such charges are included in intangible development costs,
production expenses and fees to Managing General Partner.  These charges are
allocated between the General and Limited Partners based upon applicable revenue
and expense sharing rates.

                                       8
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A LIMITED PARTNERSHIP)
                                        
               MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                      CONDITION AND RESULTS OF OPERATIONS

                                March 31, 1998


The Partnership's average price per barrel of oil for the first quarter of 1998
was $10.69 as compared to $18.44 for the first quarter of 1997. The decreased
revenue results primarily from the decrease in average oil prices.

Production expenses for 1998 increased from the comparable period in 1997, due
to an increase in the number of remedial workovers and due to an increase in the
costs of oil field services.

The Partnership was formed with cash contributions from the Limited and General
Partners.  Management does not intend to incur any substantial indebtedness and
any developmental drilling which is necessary will be processed by farmout to
other parties or by reinvestment of internally generated funds.  Management,
therefore, anticipates no liquidity problems during the life of the Partnership.

                                       9
<PAGE>
 
PART II


Items 1 through 6
-----------------

Omitted - Not applicable to Registrant.


                                   SIGNATURE
                                   ---------
                                        

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.


                                  Texland Drilling Program-1981, Ltd.



                                  By /s/ M. E. CHAPMAN
                                     -------------------------------------------
                                     M. E. Chapman, Vice President
                                     of Texland Petroleum, Inc.,
                                     General Partner - Texland
                                     Properties-1981



Date: June 3, 1998

                                       10