<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 10-Q

                  QUARTERLY REPORT UNDER SECTION 13 OR 15(d) OF
                       THE SECURITIES EXCHANGE ACT OF 1934



Quarter ended March 31, 1998                      Commission file number 0-14403


                                BRUNSWICK BANCORP
                                -----------------
             (Exact Name of Registrant as Specified in its Charter)



         NEW JERSEY                                            22-2610694
         ----------                                            ----------
(State of Other Jurisdiction of                             (I.R.S. Employer
 Incorporation or Organization)                           Identification Number)


         NEW BRUNSWICK, NEW JERSEY                                   08901
         -------------------------                                   -----
(Address of principal executive offices)                           (Zip Code)


                                 (732) 247-5800
                                 --------------
               (Registrant's Telephone Number Including Area Code)


                                 NOT APPLICABLE
                                 --------------
               (Former Name, Former Address and Former Fiscal Year
                          if Changed Since Last Report)


COMMON STOCK, PAR VALUE $2.00                              721,920 SHARES
-----------------------------                              --------------
      (Class of Stock)                           (Outstanding at March 31, 1998)




         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 periods that the
registrant was required to file such report), and (2) has been subject to such
filing requirements for the past 90 days.

                  Yes   X                         NO
                       ---                          ---
<PAGE>   2
                       BRUNSWICK BANCORP AND SUBSIDIARIES



                                    I N D E X

<TABLE>
<CAPTION>
                                                                         P A G E
<S>                                                                      <C>
PART I - FINANCIAL INFORMATION

 Item 1. Financial Statements (Unaudited):

                  Consolidated Balance Sheets
                  March 31, 1998 and December 31, 1997                       1

                  Consolidated Statements of Income
                  Three Months Ended March 31, 1998, 1997 and 1996           2

                  Consolidated Statements of Stockholders' Equity
                  Three Months Ended March 31, 1998, 1997 and 1996           3

                  Consolidated Statements of Cash Flows
                  Three Months Ended March 31, 1998, 1997 and 1996           4

                  Notes to Consolidated Financial Statements               5-6

 Item 2. Management's Discussion and Analysis of Financial
                   Conditions and Results of Operations                    7-8


PART II - OTHER INFORMATION

 Item 6. Exhibits and Reports on Form 8-K                                    9


 Signatures                                                                 10
</TABLE>
<PAGE>   3
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEETS
                                    UNAUDITED

<TABLE>
<CAPTION>
                                                           MAR 31                  DEC 31
                                                            1998                    1997
                                                       -------------           -------------
<S>                                                    <C>                     <C>
ASSETS:
    Cash and due from banks                            $   9,229,667           $   4,933,343
    Federal funds sold                                    29,100,000              26,600,000
    Securities held to maturity                           12,053,149              15,120,064
    Loans receivable, net                                 50,319,916              52,705,619
    Premises and equipment                                 1,564,457               1,252,328
    Foreclosed real estate                                   124,337                  60,080
    Other assets                                             989,955                 968,815
                                                       -------------           -------------

           NET ASSETS                                  $ 103,381,481           $ 101,640,249
                                                       =============           =============


LIABILITIES AND STOCKHOLDERS' EQUITY:
    Liabilities:
     Deposits:
      Demand deposits                                  $  27,919,611           $  25,177,070
      NOW accounts                                        23,502,988              18,447,438
      Savings deposits                                    12,300,722              12,706,999
      Time deposits                                       18,329,752              24,426,444
                                                       -------------           -------------

           Total deposits                                 82,053,073              80,757,951
    Borrowed funds                                           314,900                 511,649
    Accrued expenses and other liabilities                   837,306                 545,074
                                                       -------------           -------------

           Total liabilities                              83,205,279              81,814,674
                                                       -------------           -------------

    Stockholders' equity:
     Common stock, par value $2.00:
      Authorized 3,000,000 shares;
      issued 721,920 shares                                1,443,840               1,443,840
     Additional paid-in capital                            4,284,804               4,284,804
     Retained earnings                                    14,521,272              14,168,828
     Treasury stock at cost                                  (73,714)                (71,897)
                                                       -------------           -------------

           Total stockholders' equity                     20,176,202              19,825,575
                                                       -------------           -------------


           TOTAL LIABILITIES AND STOCKHOLDERS
            EQUITY                                     $ 103,381,481           $ 101,640,249
                                                       =============           =============
</TABLE>


                                        1
<PAGE>   4
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                        CONSOLIDATED STATEMENTS OF INCOME
                THREE MONTHS ENDED MARCH 31, 1998, 1997 AND 1996
                                    UNAUDITED

<TABLE>
<CAPTION>
                                                   1998                1997                1996
                                                ----------          ----------          ----------
<S>                                             <C>                 <C>                 <C>
INTEREST INCOME:
    Interest and fees on loans                  $1,392,051          $1,345,664          $1,129,913
    Interest on investment securities:
     Taxable                                       193,467             222,560             232,397
     Exempt from Federal income tax                  1,091               2,100               3,031
    Interest on Federal funds sold                 364,458             229,144             295,025
                                                ----------          ----------          ----------

           Total interest income                 1,951,067           1,799,468           1,660,366
                                                ----------          ----------          ----------

INTEREST EXPENSE:
    Interest on deposits                           471,391             483,181             482,625
    Interest on borrowed funds                       3,802               3,432               4,200
                                                ----------          ----------          ----------

           Total interest expense                  475,193             486,613             486,825
                                                ----------          ----------          ----------


Net interest income                              1,475,874           1,312,855           1,173,541
Provision for credit losses                         75,000             170,000              75,000
                                                ----------          ----------          ----------

Net interest income after
 provision for credit losses                     1,400,874           1,142,855           1,098,541
                                                ----------          ----------          ----------

NON-INTEREST INCOME:
    Service fees                                   200,949             188,952             168,033
    Other non-interest income                        4,080                  --              24,035
                                                ----------          ----------          ----------

           Total non-interest income               205,029             188,952             192,068
                                                ----------          ----------          ----------

NON-INTEREST EXPENSES:
    Salaries and wages                             414,355             399,579             442,654
    Employee benefits                              125,561             109,540             110,283
    Occupancy                                      146,544             154,437             165,029
    Furniture and equipment                         40,445              40,489              35,771
    Other non-interest expenses                    314,654             290,180             281,354
                                                ----------          ----------          ----------

           Total non-interest expenses           1,041,559             994,225           1,035,091
                                                ----------          ----------          ----------

Income before income taxes                         564,344             337,582             255,518
Income tax expense                                 211,900             156,480             113,887
                                                ----------          ----------          ----------

NET INCOME                                      $  352,444          $  181,102          $  141,631
                                                ==========          ==========          ==========


NET INCOME PER SHARE                            $      .49          $      .25          $      .20
                                                ==========          ==========          ==========
</TABLE>

                                        2
<PAGE>   5
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                 CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY
                THREE MONTHS ENDED MARCH 31, 1998, 1997 AND 1996
                                    UNAUDITED

<TABLE>
<CAPTION>
                                    COMMON                                     RETAINED            TREASURY
                                    STOCK                 SURPLUS              EARNINGS              STOCK              TOTAL
                                 ------------          ------------          ------------          ---------       ------------
<S>                              <C>                   <C>                 <C>                  <C>                <C>
Balance
  December 31, 1995              $  1,443,840         $  4,284,804         $ 12,161,436         $      --          $ 17,890,080

  Net income                               --                   --              141,631                --               141,631
                                 ------------         ------------         ------------         ---------          ------------

Balance
  Mar. 31, 1996                  $  1,443,840         $  4,284,804         $ 12,303,067         $      --          $ 18,031,711
                                 ============         ============         ============         =========          ============


Balance
  December 31, 1996              $  1,443,840         $  4,284,804         $ 12,924,286         $      --          $ 18,652,930

  Net income                               --                   --              181,102                --               181,102
                                 ------------         ------------         ------------         ---------          ------------

Balance
  Mar. 31, 1997                  $  1,443,840         $  4,284,804         $ 13,105,388         $      --          $ 18,834,032
                                 ============         ============         ============         =========          ============

Balance
  December 31, 1997              $  1,443,840         $  4,284,804         $ 14,168,828         $ (71,897)         $ 19,825,575

  Net income                               --                   --              352,444                --               352,444

  Purchase of
    treasury stock                         --                   --                   --            (1,817)               (1,817)
                                 ------------         ------------         ------------         ---------          ------------

Balance
  Mar. 31, 1998                  $  1,443,840         $  4,284,804         $ 14,521,272         ($ 73,714)         $ 20,176,202
                                 ============         ============         ============         =========          ============
</TABLE>

                                                                       3
<PAGE>   6
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                THREE MONTHS ENDED MARCH 31, 1998, 1997 AND 1996
                                    UNAUDITED

<TABLE>
<CAPTION>
                                               1998               1997               1996
                                          ------------       ------------       ------------
<S>                                       <C>                <C>                <C>
OPERATING ACTIVITIES:
Net income                                $    352,444       $    181,102       $    141,631
Adjustments to reconcile net
 income to cash provided by
 operating activities:
  Provision for credit losses                   75,000            170,000             75,000
      Depreciation and amortization             34,921             31,090             24,972
      Net accretion of securities
       discounts                               (81,758)           (14,528)           (13,808)
      (Increase) decrease in other
       assets                                  (21,140)          (270,299)           169,404
      Increase in accrued expenses
       and other liabilities                   292,232            218,407            141,176
                                          ------------       ------------       ------------
      CASH FLOWS FROM OPERATING
                   ACTIVITIES                  651,699            315,772            538,375
                                          ------------       ------------       ------------

INVESTING ACTIVITIES:
 Net (increase) decrease in
      Federal funds sold                    (2,500,000)        10,000,000         (4,000,000)
 Maturities of investment
      securities                             6,009,840          7,000,000          7,000,000
 Principal repayments on invest-
      ment securities                           64,303             40,266             66,468
 Purchase of investment
      securities                            (2,925,470)       (11,012,300)        (6,965,000)
 Net (increase) decrease in loans
      receivable                             2,246,446           (501,092)        (2,214,685)
 Acquisitions of premises and
      equipment                               (347,050)          (139,138)           (83,977)
                                          ------------       ------------       ------------
      CASH FLOWS FROM INVESTING
                   ACTIVITIES                2,548,069          5,387,736         (6,197,194)
                                          ------------       ------------       ------------

FINANCING ACTIVITIES:
 Net increase (decrease) in
      demand deposits                        2,742,541         (1,829,938)         1,935,293
 Net increase (decrease) in
      NOW accounts                           5,055,550         (6,710,230)         4,394,240
 Net increase (decrease) in
      savings deposits                        (406,277)          (393,785)            59,783
 Net increase (decrease) in
      time deposits                         (6,096,692)          (159,806)        (1,649,172)
 Net increase (decrease) in
      borrowed funds                          (196,749)           183,544              9,995
 Purchase of treasury stock                     (1,817)                --                 --
                                          ------------       ------------       ------------
      CASH FLOWS FROM FINANCING
                   ACTIVITIES                1,096,556         (8,910,215)         4,750,139
                                          ------------       ------------       ------------

Increase (decrease) in cash and cash
 equivalents                                 4,296,324         (3,206,707)          (908,680)
Cash and cash equivalents at
 January 1                                   4,933,343          9,190,838          6,348,014
                                          ------------       ------------       ------------
Cash and cash equivalents at
 March 31                                 $  9,229,667       $  5,984,131       $  5,439,334
                                          ============       ============       ============
</TABLE>

                                        4
<PAGE>   7
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                 MARCH 31, 1998
                                    UNAUDITED


                   NOTE 1
                   BASIS OF PRESENTATION

                   The accompanying unaudited condensed consolidated financial
                   statements have been prepared in accordance with generally
                   accepted accounting principles for interim financial
                   information, and with the instructions to Form 10-Q and Rule
                   10-01 of Regulation S-X. Accordingly, they do not include all
                   of the information and footnotes required by generally
                   accepted accounting principles for complete financial
                   statements. In the opinion of management, the information
                   presented includes all normal and recurring adjustments
                   considered necessary for a fair presentation of the interim
                   period results.



                   NOTE 2
                   INVESTMENT SECURITIES

                   The following is a comparative summary of the book values and
                   estimated market values of investment securities:

<TABLE>
<CAPTION>
                                                                                     MARCH 31, 1998
                                                                 BOOK VALUE            MARKET VALUE
<S>                                                              <C>                    <C>
                   U.S. Treasury                                 $10,113,837            $10,471,876
                   States and political subdivisions                  41,331                 41,331
                   Other securities                                1,897,981              1,920,500
                                                                  ----------             ----------

                                                                 $12,053,149            $12,433,707
                                                                  ==========             ==========
</TABLE>
<TABLE>
<CAPTION>
                                                                         DECEMBER 31, 1997
                                                                 BOOK VALUE             MARKET VALUE
<S>                                                              <C>                    <C>
                   U.S. Treasury                                 $13,168,184            $13,630,617
                   States and political subdivisions                  54,572                 54,572
                   Other securities                                1,897,308              1,923,330
                                                                  ----------             ----------

                                                                 $15,120,064            $15,608,519
                                                                  ==========             ==========
</TABLE>
                                       5
<PAGE>   8
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                 MARCH 31, 1998
                                    UNAUDITED


                   NOTE 3
                   NET LOANS

                   The composition of net loans is as follows:

<TABLE>
<CAPTION>
                                                             MARCH 31              DECEMBER 31
                                                               1998                       1997
                                                             ----------            -----------
<S>                                                         <C>                    <C>
                   Commercial loans                         $18,533,241            $19,891,202
                   Real estate loans                         31,487,789             32,467,152
                   Consumer loans                             1,336,511              1,328,652
                                                             ----------             ----------

                                                             51,357,541             53,687,006
                   Less:
                     Allowance for credit losses                894,427                820,254
                     Unearned income                            143,198                161,133
                                                             ----------             ----------

                                                            $50,319,916            $52,705,619
                                                             ==========             ==========
</TABLE>

                   NOTE 4
                   PREMISES AND EQUIPMENT

                   The major components of premises and equipment are as
                   follows:

<TABLE>
<CAPTION>
                                                             MARCH 31              DECEMBER 31
                                                               1998                    1997
                                                            -----------            ----------
<S>                                                         <C>                    <C>
                   Land                                     $   834,372            $   537,927
                   Buildings                                    562,049                562,049
                   Leasehold improvements                        70,137                 70,137
                   Equipment                                  1,075,852              1,058,097
                                                            -----------             ----------

                                                              2,542,410              2,228,210
                   Less accumulated depreciation
                    and amortization                            977,953                975,882
                                                             ----------             ----------

                                                            $ 1,564,457            $ 1,252,328
                                                             ==========             ==========
</TABLE>

                                        6
<PAGE>   9
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITIONS AND RESULTS OF OPERATIONS
                                 MARCH 31, 1998


There were no significant changes in the Corporation's Balance Sheet since
December 31, 1997; however, it should be mentioned that investment securities
decreased by approximately $3,000,000 as a result of securities being called
prior to maturity.

Also, loan balances decreased by $2,386,000, and deposits increased by
$1,295,000. The aforementioned changes resulted in increases in liquid assets,
cash and balances with banks including Federal funds sold.

Also noteworthy is an increase of approximately $74,000 in the allowance for
credit losses which resulted mainly from $75,000 in credit loss provisions. At
March 31, 1998, the allowance for credit losses represented 1.7% of total loans
and 52.3% of past due 90 days or more and nonaccrual loans.

The results of operations for the first quarter of 1998, compared to the same
period of 1997, show an increase in income before taxes of approximately
$227,000. The main reasons for this increase are a $163,000 increase in net
interest income and a decrease in the provision for credit losses of $95,000,
offset by an increase in non-interest expenses of approximately $47,000. The
increase in net interest income is analyzed in detail on page 8.

Non-interest income and expense balances were comparable to those amounts
reported for the first quarter of 1997.

The Corporation's capital position continues to be one of its strong points. At
March 31, 1998 our total risk-based capital ratios was 31.9% which is almost
four times the regulatory requirement.

In Management's opinion, the Corporation's liquidity position is strong, based
on its high level of core deposits, the stability of its other funding sources
and the support provided by its capital base.


                                        7
<PAGE>   10
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                   ANALYSIS OF CHANGES IN NET INTEREST INCOME
                                 (IN THOUSANDS)

<TABLE>
<CAPTION>
                                                              Increase (Decrease) Due to Changes in

                                                               Volume         Rates         Total
                                                                -----         -----         -----
<S>                                                           <C>             <C>           <C>
Three Months Ended March 31, 1998
           Versus
Three Months Ended March 31, 1997
Interest income on:
      Loans                                                     ($ 65)        $ 112         $  47
      Investment securities                                       (22)           (8)          (30)
      Federal funds sold                                          119            16           135
                                                                -----         -----         -----

                   Total interest income                           32           120           152
                                                                -----         -----         -----

Interest expense on:
      Deposits                                                      8           (19)          (11)
      Borrowed funds                                                0             0             0
                                                                -----         -----         -----

                   Total interest expense                           8           (19)          (11)
                                                                -----         -----         -----

                   Net interest income                          $  24         $ 139         $ 163
                                                                =====         =====         =====
</TABLE>


                                        8
<PAGE>   11
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                           PART II - OTHER INFORMATION



                   Item 6 - Exhibits and Reports on Form 8-K

                   The Corporation filed no Form 8-K during the three month
                   period ended March 31, 1998.


                                        9
<PAGE>   12
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                                   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 duly authorized.



                       BRUNSWICK BANCORP AND SUBSIDIARIES




                     04-24-98                     Carmen J. Gumina
                   ------------                   ---------------------------- 
                       Date                       Carmen J. Gumina
                                                  President




                     04-24-98                     Thomas Fornale
                   ------------                   ----------------------------
                       Date                       Thomas Fornale
                                                  Treasurer


                                       10