<PAGE>   1

                       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 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 No.
                                     0-21905


                          COULTER PHARMACEUTICAL, INC.
             (Exact name of registrant as specified in its charter)


           Delaware                                            94-3219075
(State or other jurisdiction of                               (I.R.S. Employer
 incorporation or organization)                              Identification No.)

550 California Ave, Palo Alto, California                          94306
    (Address of principal executive offices)                     (Zip Code)

Registrant's telephone number, including area code:            650-849-7500


        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  [ ]

        Number of shares outstanding of the issuer's Common Stock, par value
$.001 per share, as of May 7, 1998: 13,643,154.



                                       1
<PAGE>   2


                          COULTER PHARMACEUTICAL, INC.
                                      INDEX


<TABLE>
<CAPTION>
PART     I.    FINANCIAL INFORMATION                                             PAGE NO.
                                                                                 --------
<S>                                                                              <C>
Item     1.       Consolidated Financial Statements and Notes                          3

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

                  Consolidated Statements of Operations - Three months
                  ended March 31, 1998 and 1997 and for the period from
                  inception (February 16, 1995) to March 31, 1998                      4

                  Consolidated Statements of Cash Flows - Three months
                  ended March 31, 1998 and 1997 and for the period from
                  inception (February 16, 1995) to March 31, 1998                      5

                  Notes to Consolidated Financial Statements                           6

Item     2.       Management's Discussion and Analysis of Financial
                  Condition and Results of Operations                                  7


PART     II.   OTHER INFORMATION

Item     6.       Exhibits and Reports on Form 8-K                                    10

SIGNATURES                                                                            11
</TABLE>



                                       2
<PAGE>   3

                          PART I. FINANCIAL INFORMATION

Item 1.  Consolidated Financial Statements and Notes

                          COULTER PHARMACEUTICAL, INC.
                          (A DEVELOPMENT STAGE COMPANY)
                           CONSOLIDATED BALANCE SHEETS
               (in thousands, except share and per share amounts)

                                     ASSETS
<TABLE>
<CAPTION>
                                                                                    MARCH 31,      DECEMBER 31,
                                                                                     1998              1997
                                                                                   ---------       ------------
Current assets:                                                                   (Unaudited)        (Note 1)
<S>                                                                               <C>              <C>      
            Cash and cash equivalents                                              $  11,031        $  20,451
            Short-term investments                                                    56,340           54,994
            Prepaid expenses and other current assets                                    491              269
                                                                                   ---------        ---------

                Total current assets                                                  67,862           75,714

        Property and equipment, net                                                    2,573            2,263
        Employee loans receivable                                                        299              323
        Other assets                                                                     371              371
                                                                                   ---------        ---------
                                                                                   $  71,105        $  78,671
                                                                                   =========        =========

                      LIABILITIES AND STOCKHOLDERS' EQUITY
        Current liabilities:

            Accounts payable                                                       $   1,470        $   1,838
            Accrued liabilities                                                       10,967            7,959
            Current portion of equipment financing obligations
                and debt facility                                                        765              715
                                                                                   ---------        ---------

                Total current liabilities                                             13,202           10,512

        Non current portion of equipment financing obligations
            and debt facility                                                          2,106            2,298

        Commitments
        Stockholders' equity:
            Preferred stock, issuable in series, $.001 par value:
                  20,000,000 shares authorized;  no shares issued and
                outstanding at March  31, 1998 or December 31, 1997                       --               --
            Common stock, $.001 par value: 30,000,000 shares
                authorized; 13,629,528 shares  and 13,570,224  shares issued
                and outstanding at March  31, 1998 and December 31, l997,
                respectively                                                              14               14
            Additional paid-in capital                                               111,746          111,598
            Accumulated other comprehensive income                                       (35)              (7)
            Deferred compensation                                                     (1,004)          (1,085)
            Deficit accumulated during the development stage                         (54,924)         (44,659)
                                                                                   ---------        ---------

                Total stockholders' equity                                            55,797           65,861
                                                                                   ---------        ---------
                                                                                   $  71,105        $  78,671
                                                                                   =========        =========
</TABLE>



                             See accompanying notes.


                                       3
<PAGE>   4

                          COULTER PHARMACEUTICAL, INC.
                          (A DEVELOPMENT STAGE COMPANY)
                      CONSOLIDATED STATEMENTS OF OPERATIONS
                                   (unaudited)
                      (in thousands, except per share data)



<TABLE>
<CAPTION>
                                                                                   
                                                        THREE MONTHS ENDED           FOR THE PERIOD 
                                                              MARCH 31,              FROM INCEPTION
                                                      ------------------------     (FEBRUARY 16, 1995)
                                                        1998            1997        TO MARCH 31, 1998
                                                      --------        --------    --------------------
<S>                                                   <C>             <C>         <C>     
        Operating expenses:

            Research and development                  $  9,017        $  3,036        $ 46,282
            Selling, general and administrative          2,160           1,208          12,760
                                                      --------        --------        --------

        Total operating expenses                        11,177           4,244          59,042

        Interest income and other, net                     912             438           4,118
                                                      --------        --------        --------

        Net loss                                      $(10,265)       $ (3,806)       $(54,924 )
                                                      ========        ========        ========

        Basic and diluted net loss per share          $( 0.77 )       $( 0.56 )
                                                      --------        --------

        Shares used in computing basic
            and diluted net loss per share              13,377           6,792
                                                      ========        ========
</TABLE>



                             See accompanying notes.



                                       4
<PAGE>   5

                          COULTER PHARMACEUTICAL, INC.
                          (A DEVELOPMENT STAGE COMPANY)
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                Increase (decrease) in cash and cash equivalents
                                   (unaudited)
                                 (in thousands)



<TABLE>
<CAPTION>
                                                                                      FOR THE PERIOD
                                                            THREE MONTHS              FROM INCEPTION
                                                            ENDED MARCH 31,           (FEB. 16, 1995)
                                                         1998              1997      TO MARCH 31, 1998
                                                       ---------        ---------    ------------------
<S>                                                    <C>              <C>          <C>       
CASH FLOWS FROM OPERATING ACTIVITIES:
Net loss                                               $ (10,265)       $  (3,806)       $ (54,924)
Adjustments to reconcile net loss to net cash
    provided by (used in) operating activities:
    Depreciation and amortization                             98               22              409
    Amortization of deferred compensation                     81              298            1,496
Changes in operating assets and liabilities:
    Prepaid expenses and other current assets               (222)             (66)            (491)
    Employee loans receivable                                 24               37             (299)
    Other assets                                              --                9             (371)
    Accounts payable                                        (368)             285            1,470
    Accrued liabilities                                    3,008           (3,202)          10,967
                                                       ---------        ---------        ---------

        Net cash used in operating activities             (7,644)          (6,423)         (41,743)
                                                       ---------        ---------        ---------

CASH FLOWS FROM INVESTING ACTIVITIES:
Purchases of short-term investments                      (32,432)         (21,781)        (104,749)
Maturities of short-term investments                      25,984            7,645           41,114
Sales of short-term investments                            5,074               --            7,344
Purchases of property and equipment                         (408)            (185)          (2,978)
                                                       ---------        ---------        ---------
        Net cash used in investing activities             (1,782)         (14,321)         (59,269)
                                                       ---------        ---------        ---------

CASH FLOWS FROM FINANCING ACTIVITIES:
Payments of equipment financing obligations
    and debt facility                                       (175)             (86)            (750)
Borrowings under equipment financing
    obligations and debt facility                             33            1,159            3,533
Proceeds from issuances of convertible preferred
    stock, net                                                --               --           28,355
Proceeds from issuance of common stock, net                  148           34,445           80,905
                                                       ---------        ---------        ---------
Net cash provided by financing activities                      6           35,518          112,043
                                                       ---------        ---------        ---------
Net increase  in cash and cash equivalents                (9,420)          14,774           11,031
Cash and cash equivalents at beginning of period          20,451            8,826               --
                                                       ---------        ---------        ---------
Cash and cash equivalents at end of period             $  11,031        $  23,600        $  11,031
                                                       =========        =========        =========
</TABLE>



                             See accompanying notes


                                       5
<PAGE>   6

                          COULTER PHARMACEUTICAL, INC.
                          (A DEVELOPMENT STAGE COMPANY)

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

                                 March 31, 1998
                                   (unaudited)


1.      SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

        Basis of Presentation

        The information at March 31, 1998, for the three month periods ended
March 31, 1998 and 1997 and for the period from inception (February 16, 1995) to
March 31, 1998 is unaudited but includes all adjustments (consisting only of
normal recurring adjustments) which, in the opinion of management, are necessary
to state fairly the financial information set forth therein in accordance with
generally accepted accounting principles. The March 31, 1998 interim results are
not necessarily indicative of results to be expected for the full fiscal year.
These financial statements should be read in conjunction with the audited
financial statements for the fiscal year ended December 31, 1997 included in the
Company's annual report to security holders furnished to the Securities and
Exchange Commission pursuant to Rule 14a-3(b) in connection with the Company's
1998 Annual Meeting of Stockholders.

        The consolidated balance sheet at December 31, 1997 has been derived
from audited consolidated financial statements at that date but does not include
all of the information and footnotes required by generally accepted accounting
principles for complete financial statements.

        Net Loss Per Share

         Effective December 31, 1997 the Company adopted Statement of Financial
Accounting Standards No. 128 ("SFAS 128"), "Earnings Per Share", which modifies
the way in which earnings per share are calculated and disclosed.

        "Basic" net loss per share (as defined by SFAS 128) is computed using
the weighted average number of common shares outstanding less those shares
outstanding subject to continued vesting. As the Company reported a loss for all
periods presented, there is no difference between basic and diluted net loss per
share amounts as prescribed by SFAS 128. Loss per share for the three months
ended March 31, 1997 has been restated to conform to the requirements of SFAS
128.

        New Accounting Standard

        As of January 1, 1998, the Company adopted Statement 130, Reporting
Comprehensive Income. Statement 130 establishes new rules for the reporting and
display of comprehensive income and its components; however, the adoption of
this Statement had no impact on the Company's net income or shareholders'
equity. Statement 130 requires unrealized gains or losses on the Company's
available-for-sale securities which, prior to adoption, were reported separately
in shareholders' equity to be included in other comprehensive income. Prior year
financial statements have been reclassified to conform to the requirements of
Statement 130.

During the first quarter of 1998 and 1997, total comprehensive loss amounted to
$10.3 million and $3.9 million, respectively.



                                       6
<PAGE>   7

2.      INVESTMENTS

        Management determines the appropriate classification of debt securities
at the time of purchase and re-evaluates such designation as of each balance
sheet date. The Company's debt securities are classified as available-for-sale
and are carried at estimated fair value in cash equivalents and short-term
investments. Unrealized gains and losses are reported as accumulated other
comprehensive income in stockholders' equity. The amortized cost of debt
securities in this category is adjusted for amortization of premiums and
accretion of discounts to maturity. Such amortization is included in interest
income. Realized gains and losses on available-for-sale securities are included
in interest income and expense. The cost of securities sold is based on the
specific identification method. Interest and dividends on securities classified
as available-for-sale are included in interest income. The Company's cash
equivalents and short-term investments as of March 31, 1998 are as follows (in
thousands):

<TABLE>
<CAPTION>
                                                         GROSS            GROSS
                                    AMORTIZED          UNREALIZED       UNREALIZED         ESTIMATED
                                      COST               GAINS            LOSSES           FAIR VALUE
                                   -------------------------------------------------------------------
<S>                                <C>                <C>               <C>                <C>        
Money market funds                 $     1,943        $        --       $        --        $     1,943
Commercial paper                        20,571                 --               (16)            20,555
Corporate bond                          24,117                 --               (10)            24,107
Certificate of Deposits                 20,636                 --                (9)            20,627
                                   -----------        -----------       -----------        -----------

      Total                             67,267                 --               (35)            67,232

Less amounts classified
      as cash equivalents              (10,898)                --                 6            (10,892)
                                   -----------        -----------       -----------        -----------

Total short-term investments       $    56,369        $        --       $       (29)       $    56,340
                                   ===========        ===========       ===========        ===========
</TABLE>

Realized gain or losses of available-for-sale securities for the quarter ended
March 31, 1998 were not significant. There were no realized gains or losses on
the sale of available-for-sale securities for the quarter ended March 31, 1997.

At March 31, 1998 the contractual maturities of short term investments were as
follows (in thousands):

<TABLE>
<CAPTION>
                                                            ESTIMATED FAIR
                                           AMORTIZED COST       VALUE
                                           --------------   --------------
<S>                                        <C>              <C>    
Due in one year or less                       $30,944          $30,925
Due after one year through two years           25,425           25,415
                                              -------          -------
                                              $56,369          $56,340
                                              =======          =======
</TABLE>



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

        The following discussion contains, in addition to historical
information, forward-looking statements that involve risks and uncertainties.
Actual results may differ significantly from the results discussed in the
forward-looking statements. Factors that could cause or contribute to such
differences include, but are not limited to, those discussed below and in the
Company's Annual Report on Form 10-K for the year ended December 31, 1997.



                                       7
<PAGE>   8

OVERVIEW

        Coulter Pharmaceutical is engaged in the development of novel drugs and
therapies for the treatment of people with cancer. The Company currently is
developing a family of cancer therapeutics based upon two drug discovery
programs, therapeutic antibodies and targeted oncologics. Within these broad
discovery programs, the Company is currently concentrating on two distinct
platform technologies: therapeutic antibodies based on conjugated antibody
technology and targeted oncologics based on tumor activated peptide pro-drugs.

The Company's most advanced product candidate, Bexxar (formerly known as the
"B-1 Therapy"), consists of a monoclonal antibody conjugated with a
radioisotope. The Company intends to seek initial approval of Bexxar for the
treatment of low-grade and transformed low-grade non-Hodgkin's lymphoma ("NHL")
in patients refractory to chemotherapy, while simultaneously pursuing clinical
trials to expand the potential use of Bexxar to other indications. Bexxar is
based upon the antibody therapeutics program which originated at Coulter
Corporation. In 1995 Coulter Pharmaceutical was incorporated and acquired
worldwide rights to Bexxar and related intellectual property, know-how and other
assets from Coulter Corporation. In 1997 Beckman Instruments, Inc. acquired
Coulter Corporation upon which occurrence Coulter Corporation became known as
Beckman Coulter ("Beckman Coulter").

        To date, the Company has devoted substantially all of its resources to
its research and development programs, as well as selling, general and
administrative activities needed to support product development and potential
product sales. No revenues have been generated from product sales, and products
resulting from the Company's research and development efforts, if any, are not
expected to be available commercially for at least the next one to two years.
The Company has a limited history of operations and has experienced significant
operating losses to date. The Company expects to incur significant additional
operating losses over the next several years and expects cumulative losses to
increase substantially due to expanded research and development efforts,
preclinical studies and clinical trials and development of manufacturing,
marketing and sales capabilities. The Company expects that losses will fluctuate
from quarter to quarter and that such fluctuations may be substantial. There can
be no assurance that the Company will successfully develop, manufacture and
commercialize its products or ever achieve or sustain product revenues or
profitability. As of March 31, 1998, the Company's accumulated deficit during
the development stage was approximately $54.9 million.

RESULTS OF OPERATIONS

Operating Costs and Expenses

        Research and development expenses were $9.0 million for the quarter
ended March 31, 1998, compared to $3.0 million for the same period in 1997. This
$6.0 million increase was due primarily to increases in staffing and
expenditures associated with the development of Bexxar, including costs of
clinical trials and manufacturing expenses. These manufacturing expenses
included certain expenses associated with scaled-up production of monoclonal
antibodies and the establishment of a centralized radiolabeling capability. The
Company expects its research and development expenses to continue to grow during
the remainder of 1998, reflecting anticipated increased costs related to
additions to staffing, preclinical studies, clinical trials and manufacturing.

        Selling, general and administrative expenses were $2.2 million for the
quarter ended March 31, 1998, compared to $1.2 million for the same period in
1997. This $1.0 million increase was incurred to support the Company's
facilities and staffing expansion, increased research and development efforts,
increased pre-commercialization activities, increased corporate development
activities and related legal and patent activities. The Company expects its
selling, general and administrative expenses to continue to increase during the
remainder of 1998, in support of its increased research and development, patent
and corporate development 



                                       8

<PAGE>   9

activities, as well as increasing commercialization efforts in anticipation of
potential product sales.

Interest Income and Other, net

         Interest income was $912,000 for the quarter ended March 31, 1998,
compared to $438,000 for the same period in 1997. This increase was due to
higher average cash, cash equivalent and short-term investment balances as a
result of the completion of the Company's initial public offering in January
1997 and follow-on offering in October 1997.

LIQUIDITY AND CAPITAL RESOURCES

        Since its inception through March 31, 1998, the Company has financed its
operations primarily through private placements and public offerings of equity
securities totaling $109.3 million. In addition, the Company entered into a $3.8
million equipment lease financing and debt facility in December 1996, $0.3
million of which is available at March 31, 1998. Cash, cash equivalents and
short-term investments totaled $67.4 million at March 31, 1998.

        The negative cash flow from operations results primarily from the
Company's net operating losses and is expected to continue and to accelerate in
the foreseeable future. The Company expects to incur substantial and increasing
research and development expenses, including expenses related to additions to
personnel, preclinical studies, clinical trials, manufacturing and
commercialization efforts. The Company will need to raise substantial additional
capital to fund its operations. The Company intends to seek such additional
funding through public or private equity or debt financings from time to time,
as market conditions permit. There can be no assurance that additional financing
will be available on acceptable terms, if at all. If adequate funds are not
available, the Company may be required to delay, reduce the scope of, or
eliminate one or more of its research and development programs or obtain funds
through arrangements with collaborative partners or others that may require the
Company to relinquish rights to certain of its technologies, product candidates
or products that the Company would otherwise seek to develop or commercialize.

        Net cash used in operations was $7.6 million for the quarter ended March
31, 1998, compared to $6.4 million for the same period in 1997. This $1.2
million increase is primarily the result of the increased net loss for the
quarter ended March 31, 1998, partially offset by an increase in accrued
liabilities. Net cash used in investing activities decreased to $1.8 million for
the quarter ended March 31, 1998 from $14.3 million for the same period in 1997
primarily resulting from the purchase of $32.4 million short-term investments,
partially offset by an increase in maturities of short-term investments.

        The Company expects that its existing capital resources, including the
net proceeds of its public offerings and interest thereon, will be adequate to
satisfy the requirements of its current and planned operations into 1999. At
March 31, 1998, the Company had entered into a long-term lease obligation for
office and laboratory space that will require material commitments for capital
expenditures. The Company's future capital requirements will depend on a number
of factors, including: the scope and results of preclinical studies and clinical
trials; continued progress of the Company's research and development of
potential products; the cost, timing and outcome of regulatory approvals; the
expenses of establishing a sales and marketing force; the timing and cost of
establishment or procurement of requisite production, radiolabeling and other
manufacturing capacities; the cost involved in preparing, filing, prosecuting,
maintaining, defending and enforcing patent claims; the need to acquire licenses
to new technology; the status of competitive products; and the availability of
other financing.



                                       9

<PAGE>   10

IMPACT OF THE YEAR 2000

        At this time, the Company believes that with upgrades of existing
software and conversions to new software, both of which are readily available in
the market, the Year 2000 issue will not pose significant operational problems
for its internal computer systems. Modifications and conversions to the
Company's internal computer systems are expected to be completed not later than
September 30, 1999. Some risks associated with the Year 2000 issue are beyond
the ability of the Company to control, for example, the extent to which the
Company's suppliers and service providers, including providers of telephone
services, address the Year 2000 issue. A failure by a third party to adequately
address the Year 2000 issue would have a material adverse impact on such third
party, and could result in a material adverse impact on the Company. The
Company, however, has initiated formal communications with its significant
suppliers and service providers to determine the extent to which the Company may
be vulnerable to those third parties' failure to remediate their own Year 2000
issues. The Company does not expect the estimated cost of implementing its Year
2000 plan to be significant.

BUSINESS RISKS

        Except for the historical information contained herein, the matters
discussed in this filing are forward-looking statements that involve risks and
uncertainties, including uncertainties related to product development,
uncertainties related to the need for regulatory and other government approvals,
dependence on proprietary technology, uncertainty of market acceptance of Bexxar
(TM) or the Company's other product candidates and other risks, including those
detailed in the Company's other filings with the Securities and Exchange
Commission. In particular, see "Item 1, Business-Risk Factors," of the Company's
Annual Report on Form 10-K for the year ended December 31, 1997.

                           PART II. OTHER INFORMATION

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

(a)   Exhibits

<TABLE>
<CAPTION>
      Exhibit Number               Description of Document
      --------------               -----------------------
<S>                                <C>
      27.0                         Financial Data Schedule
</TABLE>

(b)   Reports on Form 8-K

      There were no reports on Form 8-K filed during the quarter ended March 31,
1998.



                                       10
<PAGE>   11

                                   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.



                                           COULTER PHARMACEUTICAL, INC.



Date:   May 12, 1998                       /s/ MICHAEL F. BIGHAM
                                           -------------------------------------
                                           Michael F. Bigham
                                           President and Chief Executive Officer



Date:   May 12, 1998                       /s/ WILLIAM G. HARRIS
                                           -------------------------------------
                                           William G. Harris
                                           Vice President and
                                           Chief Financial Officer



                                       11
<PAGE>   12

<TABLE>
<CAPTION>
                     Exhibit
                     Number                    Description of Document
                     ------                    -----------------------
<S>                                            <C>
                      27.0                     Financial Data Schedule
</TABLE>






                                       12