<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 June 30, 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 June 30, 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




                                                                      P A G E

PART I - FINANCIAL INFORMATION

 Item 1. Financial Statements (Unaudited):

                  Consolidated Balance Sheets
                  June 30, 1998 and December 31, 1997                     1

                  Consolidated Statements of Income
                  Six Months Ended June 30, 1998, 1997 and 1996           2

                  Consolidated Statements of Income
                  Quarters Ended June 30, 1998, 1997 and 1996             3

                  Consolidated Statements of Stockholders' Equity
                  Six Months Ended June 30, 1998, 1997 and 1996           4

                  Consolidated Statements of Cash Flows
                  Six Months Ended June 30, 1998, 1997 and 1996           5

                  Notes to Consolidated Financial Statements             6-7

 Item 2. Management's Discussion and Analysis of Financial
                   Conditions and Results of Operations                  8-9


PART II - OTHER INFORMATION

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


 Signatures                                                              11




<PAGE>   3
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEETS
                                    UNAUDITED

<TABLE>
<CAPTION>
                                                              JUNE 30               DEC 31
                                                                1998                 1997
                                                                ----                 ----
ASSETS:
<S>                                                        <C>                  <C>          
    Cash and due from banks                                $   7,898,507        $   4,933,343
    Federal funds sold                                        32,700,000           26,600,000
    Securities held to maturity                               12,211,171           15,120,064
    Loans receivable, net                                     49,893,831           52,705,619
    Premises and equipment                                     1,527,328            1,252,328
    Foreclosed real estate                                       124,337               60,080
    Other assets                                                 970,801              968,815
                                                           -------------        -------------

           TOTAL ASSETS                                    $ 105,325,975        $ 101,640,249
                                                           =============        =============


LIABILITIES AND STOCKHOLDERS' EQUITY:
    Liabilities:
     Deposits:
      Demand deposits                                      $  29,813,109        $  25,177,070
      NOW accounts                                            25,056,243           18,447,438
      Savings deposits                                        12,126,288           12,706,999
      Time deposits                                           16,703,297           24,426,444
                                                           -------------        -------------

           Total deposits                                     83,698,937           80,757,951
    Borrowed funds                                               526,751              511,649
    Accrued expenses and other liabilities                       620,447              545,074
                                                           -------------        -------------

           Total liabilities                                  84,846,135           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                                        14,838,590           14,168,828
     Treasury stock at cost                                      (87,394)             (71,897)
                                                           -------------        -------------

           Total stockholders' equity                         20,479,840           19,825,575
                                                           -------------        -------------


           TOTAL LIABILITIES AND STOCKHOLDERS EQUITY       $ 105,325,975        $ 101,640,249
                                                           =============        =============
</TABLE>


                                        1
<PAGE>   4
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                        CONSOLIDATED STATEMENTS OF INCOME
                  SIX MONTHS ENDED JUNE 30, 1998, 1997 AND 1996
                                    UNAUDITED


<TABLE>
<CAPTION>
                                                   1998            1997             1996
                                                   ----            ----             ----
INTEREST INCOME:
<S>                                          <C>              <C>              <C>       
    Interest and fees on loans               $2,722,512       $2,827,851       $2,510,764
    Interest on investment securities:
     Taxable                                    370,516          519,398          436,321
     Exempt from Federal income tax               1,918            3,955            5,837
    Interest on Federal funds sold              827,239          451,353          563,321
                                             ----------       ----------       ----------

           Total interest income              3,922,185        3,802,557        3,516,243
                                             ----------       ----------       ----------

INTEREST EXPENSE:
    Interest on deposits                        979,800          967,928          967,166
    Interest on borrowed funds                    6,534            7,018            6,593
                                             ----------       ----------       ----------

           Total interest expense               986,334          974,946          973,759
                                             ----------       ----------       ----------


Net interest income                           2,935,851        2,827,611        2,542,484
Provision for credit losses                     150,000          360,000          210,000
                                             ----------       ----------       ----------

Net interest income after
 provision for credit losses                  2,785,851        2,467,611        2,332,484
                                             ----------       ----------       ----------

NON-INTEREST INCOME:
    Service fees                                414,822          425,561          349,712
    Other non-interest income                    11,394               --           34,651
                                             ----------       ----------       ----------

           Total non-interest income            426,216          425,561          384,363
                                             ----------       ----------       ----------

NON-INTEREST EXPENSES:
    Salaries and wages                          831,348          823,641          891,709
    Employee benefits                           249,344          227,407          223,475
    Occupancy                                   288,013          322,781          341,630
    Furniture and equipment                     110,387           94,306           78,821
    Other non-interest expenses                 605,629          609,745          592,237
                                             ----------       ----------       ----------

           Total non-interest expenses        2,084,721        2,077,880        2,127,872
                                             ----------       ----------       ----------

Income before income taxes                    1,127,346          815,292          588,975
Income tax expense                              457,584          357,419          251,636
                                             ----------       ----------       ----------

NET INCOME                                   $  669,762       $  457,873       $  337,339
                                             ==========       ==========       ==========


NET INCOME PER SHARE                         $      .93       $      .63       $      .47
                                             ==========       ==========       ==========
</TABLE>





                                        2
<PAGE>   5
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                        CONSOLIDATED STATEMENTS OF INCOME
                   QUARTERS ENDED JUNE 30, 1998, 1997 AND 1996
                                    UNAUDITED


<TABLE>
<CAPTION>
                                                   1998             1997             1996
                                                   ----             ----             ----
INTEREST INCOME:
<S>                                          <C>              <C>              <C>       
    Interest and fees on loans               $1,330,461       $1,482,187       $1,380,851
    Interest on investment securities:
     Taxable                                    177,049          296,838          203,924
     Exempt from Federal income tax                 827            1,855            2,806
    Interest on Federal funds sold              462,781          222,209          268,296
                                             ----------       ----------       ----------

           Total interest income              1,971,118        2,003,089        1,855,877
                                             ----------       ----------       ----------

INTEREST EXPENSE:
    Interest on deposits                        508,409          484,747          484,541
    Interest on borrowed funds                    2,732            3,586            2,393
                                             ----------       ----------       ----------

           Total interest expense               511,141          488,333          486,934
                                             ----------       ----------       ----------


Net interest income                           1,459,977        1,514,756        1,368,943
Provision for credit losses                      75,000          190,000          135,000
                                             ----------       ----------       ----------

Net interest income after
 provision for credit losses                  1,384,977        1,324,756        1,233,943
                                             ----------       ----------       ----------

NON-INTEREST INCOME:
    Service fees                                213,873          236,609          181,679
    Other non-interest income                     7,314               --           10,616
                                             ----------       ----------       ----------

           Total non-interest income            221,187          236,609          192,295
                                             ----------       ----------       ----------

NON-INTEREST EXPENSES:
    Salaries and wages                          416,993          424,062          449,055
    Employee benefits                           123,783          117,867          113,192
    Occupancy                                   141,469          168,344          176,601
    Furniture and equipment                      69,942           53,817           43,050
    Other non-interest expenses                 290,975          319,565          310,883
                                             ----------       ----------       ----------

           Total non-interest expenses        1,043,162        1,083,655        1,092,781
                                             ----------       ----------       ----------

Income before income taxes                      563,002          477,710          333,457
Income tax expense                              245,684          200,939          137,749
                                             ----------       ----------       ----------

NET INCOME                                   $  317,318       $  276,771       $  195,708
                                             ==========       ==========       ==========


NET INCOME PER SHARE                         $      .44       $      .36       $      .27
                                             ==========       ==========       ==========
</TABLE>


                                        3
<PAGE>   6
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                 CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY
                  SIX MONTHS ENDED JUNE 30, 1998, 1997 AND 1996
                                    UNAUDITED


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

  Net income                        --                 --            337,339                 --             337,339
                          ------------       ------------       ------------       ------------        ------------

Balance
  June 30, 1996           $  1,443,840       $  4,284,804       $ 12,498,775       $         --        $ 18,227,419
                          ============       ============       ============       ============        ============


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

  Net income                        --                 --            457,873                 --             457,873
                          ------------       ------------       ------------       ------------        ------------

Balance
  June 30, 1997           $  1,443,840       $  4,284,804       $ 13,382,159       $         --        $ 19,110,803
                          ============       ============       ============       ============        ============

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

  Net income                        --                 --            669,762                 --             669,762

  Purchase of
    treasury stock                  --                 --                 --            (15,497)            (15,497)
                          ------------       ------------       ------------       ------------        ------------

Balance
  June 30, 1998           $  1,443,840       $  4,284,804       $ 14,838,590       $    (87,394)       $ 20,479,840
                          ============       ============       ============       ============        ============
</TABLE>


                                        4
<PAGE>   7
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                  SIX MONTHS ENDED JUNE 30, 1998, 1997 AND 1996
                                    UNAUDITED

<TABLE>
<CAPTION>
                                                           1998                 1997                1996
                                                           ----                 ----                ----
OPERATING ACTIVITIES:
<S>                                                 <C>                 <C>                 <C>         
Net income                                          $    669,762        $    457,873        $    337,339
Adjustments to reconcile net
 income to cash provided by
 operating activities:
  Provision for credit losses                            150,000             360,000             210,000
      Depreciation and amortization                       68,894              71,388              53,775
      Net accretion of securities
       discounts                                        (172,497)            (24,583)            (37,106)
      (Increase) decrease in other
    assets                                                (1,986)           (419,984)             20,340
      Increase (decrease) in accrued
       expenses and other liabilities                     75,373              63,071             (35,340)
                                                    ------------        ------------        ------------

                   NET CASH PROVIDED BY
                    OPERATING ACTIVITIES                 789,546             507,765             549,008
                                                    ------------        ------------        ------------

INVESTING ACTIVITIES:
 Net (increase) decrease in
      Federal funds sold                              (6,100,000)         (5,100,000)           (900,000)
 Maturities of investment
      securities                                      10,009,840          12,000,000           7,000,000
 Principal repayments on invest-
      ment securities                                    151,420              83,847             142,638
 Purchases of investment
      securities                                      (7,079,870)        (11,012,300)         (6,965,000)
 Net (increase) decrease in loans
      receivable                                       2,597,531          (1,564,447)         (6,002,429)
 Acquisitions of premises and
      equipment                                         (343,894)           (139,138)           (256,400)
                                                    ------------        ------------        ------------

                   NET CASH PROVIDED BY
                    INVESTING ACTIVITIES                (764,973)         (5,732,038)         (6,981,191)
                                                    ------------        ------------        ------------

FINANCING ACTIVITIES:
 Net increase (decrease) in:
      Demand deposits                                  4,636,039             (18,751)            478,821
      NOW accounts                                     6,608,805           1,123,531           3,670,309
      Savings deposits                                  (580,711)           (750,680)           (408,924)
      Time deposits                                   (7,723,147)          2,394,706             854,319
      Borrowed funds                                      15,102             203,485             165,739
      Purchase of treasury stock                         (15,497)                 --                  --
                                                    ------------        ------------        ------------

                   NET CASH PROVIDED BY (USED
                    IN) FINANCING ACTIVITIES           2,940,591           2,952,291           4,760,264
                                                    ------------        ------------        ------------

Increase (decrease) in cash and cash
 equivalents                                           2,965,164          (2,271,982)         (1,671,919)
Cash and Cash equivalents at
 January 1                                             4,933,343           9,190,838           6,348,014
                                                    ------------        ------------        ------------

Cash and Cash equivalents at
 June 30                                            $  7,898,507        $  6,918,856        $  4,676,095
                                                    ============        ============        ============
</TABLE>

                                        5
<PAGE>   8
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                  JUNE 30, 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>
                                                                             JUNE 30, 1998
                                                           BOOK VALUE        MARKET VALUE

<S>                                                        <C>               <C>        
                   U.S. Government Agencies                $10,134,691       $10,600,700
                   States and political subdivisions            27,826            27,826
                   Other securities                          2,048,654         2,067,755
                                                           -----------       -----------
                                                           $12,211,171       $12,696,281
                                                           ===========       ===========
</TABLE>



<TABLE>
<CAPTION>
                                                                DECEMBER 31, 1997
                                                            BOOK VALUE      MARKET VALUE
<S>                                                        <C>               <C>        
                   U.S. Government Agencies                $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>




                                        6
<PAGE>   9
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                  JUNE 30, 1998
                                    UNAUDITED


                   NOTE 3
                   NET LOANS

                   The composition of net loans is as follows:

<TABLE>
<CAPTION>
                                                         JUNE 30         DECEMBER 31
                                                          1998              1997
                                                       -----------       -----------
<S>                                                    <C>               <C>        
                   Commercial loans                    $17,140,678       $19,891,202
                   Real estate loans                    32,566,970        32,467,152
                   Consumer loans                        1,324,043         1,328,652
                                                       -----------       -----------

                                                        51,031,691        53,687,006
                   Less:
                     Allowance for credit losses           980,019           820,254
                     Unearned income                       157,841           161,133
                                                       -----------       -----------

                                                       $49,893,831       $52,705,619
                                                       ===========       ===========
</TABLE>

                   NOTE 4
                   PREMISES AND EQUIPMENT

                   The major components of premises and equipment are as
                   follows:

<TABLE>
<CAPTION>
                                                       JUNE 30          DECEMBER 31
                                                         1998              1997
                                                       ----------       ----------
<S>                                                    <C>              <C>       
                   Land                                $  834,372       $  537,927
                   Buildings                              562,049          562,049
                   Leasehold improvements                  70,137           70,137
                   Equipment                            1,060,483        1,058,097
                                                       ----------       ----------

                                                        2,527,041        2,228,210
                   Less accumulated depreciation
                    and amortization                      999,713          975,882
                                                       ----------       ----------

                                                       $1,527,328       $1,252,328
                                                       ==========       ==========
</TABLE>


                                        7
<PAGE>   10
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITIONS AND RESULTS OF OPERATIONS
                                  JUNE 30, 1998


The most significant changes in the Corporation's Balance Sheet since December
31, 1997 are summarized as follows:

Investment securities and loans decreased by approximately $2,900,000 and
$2,800,000, respectively. The funds made available by these decreases were
invested in Federal funds which, for the most part, explains the $6,100,000
increase in Federal funds sold.

On the liability side of the balance sheet, time deposits decreased by
$7,700,000. However, demand deposits and NOW accounts increased by $4,600,000
and $6,600,000, respectively. These increases more than offset the decrease in
time deposits and resulted in an increase in total deposits of approximately
$2,900,000.

Also noteworthy is an increase of approximately $160,000 in the allowance for
credit losses which resulted mainly from $150,000 in credit loss provisions. At
June 30, 1998 the allowance for credit losses represented 1.9% of total loans
and 119% of loans past due 90 days or more and nonaccrual loans.

The results of operations for the first half of 1998, compared to the same
period of 1997, show an increase in income before taxes of approximately
$312,000. The main reasons for this increase are a $198,000 increase in net
interest income and a decrease in the provision for credit losses of $210,000.
The increase in net interest income is analyzed in detail on page 9.

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

The Corporation's capital position continues to be one of its strong points. At
June 30, 1998 our total risk-based capital ratio was 32.5% which is over 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.


                                        8
<PAGE>   11
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                   ANALYSIS OF CHANGES IN NET INTEREST INCOME
                                 (IN THOUSANDS)



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

                                                    Volume        Rates         Total
                                                    ------        -----         -----
Six Months Ended June 30, 1998
                    Versus
Six Months Ended June 30, 1997
Interest income on:
<S>                                                   <C>          <C>          <C>   
      Loans                                           $(137)       $  32        $(105)
      Investment securities                            (114)         (37)        (151)
      Federal funds sold                                353           23          376
                                                      -----        -----        -----

                   Total interest income                102           18          120
                                                      -----        -----        -----

Interest expense on:
      Deposits                                           31          (19)          12
      Borrowed funds                                     (1)           1           --
                                                      -----        -----        -----

                   Total interest expense                30          (18)          12
                                                      -----        -----        -----

                   Net interest income                $  72        $  36        $ 108
                                                      =====        =====        =====


Quarter Ended June 30, 1998
                    Versus
Quarter Ended June 30, 1997 
Interest income on:
      Loans                                           $ (71)       $ (81)       $(152)
      Investment securities                             (28)         (93)        (121)
      Federal funds sold                                  4          237          241
                                                      -----        -----        -----

                   Total interest income                (95)          63          (32)
                                                      -----        -----        -----

Interest expense on:
      Deposits                                           24           (1)          23
      Borrowed funds                                     --           --           --
                                                      -----        -----        -----

                   Total interest expense                24           (1)          23
                                                      -----        -----        -----

                   Net interest income                $(119)       $  64        $ (55)
                                                      =====        =====        =====
</TABLE>


                                        9
<PAGE>   12
                       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 six month period
                   ended June 30, 1998.



                                       10
<PAGE>   13
                       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




7/15/98                                                     Carmen J. Gumina
   Date                                                     Carmen J. Gumina
                                                            President




7/15/98                                                     Thomas Fornale
   Date                                                     Thomas Fornale
                                                            Treasurer

                                       11