<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 September 30, 1998                  Commission file number 0-14403


                                BRUNSWICK BANCORP

             (Exact Name of Registrant as Specified in its Charter)

<TABLE>
<CAPTION>
<S>                                                       <C>
         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)
</TABLE>

                                 (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)

<TABLE>
<S>                                          <C>
COMMON STOCK, PAR VALUE $2.00                           721,920 SHARES
         (Class of Stock)                    (Outstanding at September 30, 1998)
</TABLE>

         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
                  September 30, 1998 and December 31, 1997                            1

                  Consolidated Statements of Income
                  Nine Months Ended September 30, 1998, 1997 and 1996                 2

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

                  Consolidated Statements of Stockholders' Equity
                  Nine Months Ended September 30, 1998, 1997 and 1996                 4

                  Consolidated Statements of Cash Flows
                  Nine Months Ended September 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
</TABLE>
<PAGE>   3
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEETS
                                    UNAUDITED

<TABLE>
<CAPTION>
                                                                   SEP 30                    DEC 31
                                                                    1998                      1997
                                                                -------------             -------------
<S>                                                             <C>                       <C>
ASSETS:
    Cash and due from banks                                     $   6,304,201             $   4,933,343
    Federal funds sold                                             38,500,000                26,600,000
    Securities held to maturity                                     9,133,031                15,120,064
    Loans receivable, net                                          49,612,884                52,705,619
    Premises and equipment                                          1,494,034                 1,252,328
    Foreclosed real estate                                             60,080                    60,080
    Other assets                                                    1,060,029                   968,815
                                                                -------------             -------------

           TOTAL ASSETS                                         $ 106,164,259             $ 101,640,249
                                                                =============             =============


LIABILITIES AND STOCKHOLDERS' EQUITY:
    Liabilities:
     Deposits:
      Demand deposits                                           $  24,820,124             $  25,177,070
      NOW accounts                                                 31,727,717                18,447,438
      Savings deposits                                             12,193,195                12,706,999
      Time deposits                                                15,459,973                24,426,444
                                                                -------------             -------------

           Total deposits                                          84,201,009                80,757,951
    Borrowed funds                                                    423,127                   511,649
    Accrued expenses and other liabilities                            718,460                   545,074
                                                                -------------             -------------

           Total liabilities                                       85,342,596                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                                             15,186,173                14,168,828
     Treasury stock at cost, 327 shares                               (93,154)                  (71,897)
                                                                -------------             -------------

           Total stockholders' equity                              20,821,663                19,825,575
                                                                -------------             -------------


           TOTAL LIABILITIES AND STOCKHOLDERS EQUITY            $ 106,164,259             $ 101,640,249
                                                                =============             =============
</TABLE>

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

<TABLE>
<CAPTION>
                                                     1998                   1997                  1996
                                                     ----                   ----                  ----
<S>                                               <C>                   <C>                   <C>
INTEREST INCOME:
    Interest and fees on loans                    $4,085,065            $4,207,030            $3,791,718
    Interest on investment securities:
     Taxable                                         534,190               790,771               638,166
     Exempt from Federal income tax                    2,475                 5,560                 8,441
    Interest on Federal funds sold                 1,358,738               779,785               866,174
                                                  ----------            ----------            ----------

           Total interest income                   5,980,468             5,783,146             5,304,499
                                                  ----------            ----------            ----------

INTEREST EXPENSE:
    Interest on deposits                           1,489,110             1,472,021             1,478,535
    Interest on borrowed funds                         9,593                10,462                10,178
                                                  ----------            ----------            ----------

           Total interest expense                  1,498,703             1,482,483             1,488,713
                                                  ----------            ----------            ----------


Net interest income                                4,481,765             4,300,663             3,815,786
Provision for credit losses                          225,000               435,000               350,000
                                                  ----------            ----------            ----------

Net interest income after
 provision for credit losses                       4,256,765             3,865,663             3,465,786
                                                  ----------            ----------            ----------

NON-INTEREST INCOME:
    Service fees                                     611,140               652,540               539,586
    Other non-interest income                         15,474                  --                  55,824
                                                  ----------            ----------            ----------

           Total non-interest income                 626,614               652,540               595,410
                                                  ----------            ----------            ----------

NON-INTEREST EXPENSES:
    Salaries and wages                             1,272,494             1,228,921             1,314,008
    Employee benefits                                359,011               331,894               322,282
    Occupancy                                        433,336               545,551               503,422
    Furniture and equipment                          169,086               145,026               136,622
    Loss on foreclosed real estate                      --                 398,681                  --
    Other non-interest expenses                      886,023               987,319               872,235
                                                  ----------            ----------            ----------

           Total non-interest expenses             3,119,950             3,637,392             3,148,569
                                                  ----------            ----------            ----------

Income before income taxes                         1,763,429               880,811               912,627
Income tax expense                                   746,084               409,359               389,935
                                                  ----------            ----------            ----------

NET INCOME                                        $1,017,345            $  471,452            $  522,692
                                                  ==========            ==========            ==========


NET INCOME PER SHARE                              $     1.41            $      .65            $      .72
                                                  ==========            ==========            ==========
</TABLE>

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

<TABLE>
<CAPTION>
                                                     1997                  1996                   1995
                                                     ----                  ----                   ----
<S>                                               <C>                   <C>                   <C>
INTEREST INCOME:
    Interest and fees on loans                    $1,362,553            $1,379,179            $1,280,954
    Interest on investment securities:
     Taxable                                         163,674               271,373               201,845
     Exempt from Federal income tax                      557                 1,605                 2,604
    Interest on Federal funds sold                   531,499               328,432               302,853
                                                  ----------            ----------            ----------

           Total interest income                   2,058,283             1,980,589             1,788,256
                                                  ----------            ----------            ----------

INTEREST EXPENSE:
    Interest on deposits                             509,310               504,093               511,369
    Interest on borrowed funds                         3,059                 3,444                 3,585
                                                  ----------            ----------            ----------

           Total interest expense                    512,369               507,537               514,954
                                                  ----------            ----------            ----------


Net interest income                                1,545,914             1,473,052             1,273,302
Provision for credit losses                           75,000                75,000               140,000
                                                  ----------            ----------            ----------

Net interest income after
 provision for credit losses                       1,470,914             1,398,052             1,133,302
                                                  ----------            ----------            ----------

NON-INTEREST INCOME:
    Service fees                                     196,318               226,979               189,874
    Other non-interest income                          4,080                  --                  21,173
                                                  ----------            ----------            ----------

           Total non-interest income                 200,398               226,979               211,047
                                                  ----------            ----------            ----------

NON-INTEREST EXPENSES:
    Salaries and wages                               441,146               405,280               422,299
    Employee benefits                                109,667               104,487                98,807
    Occupancy                                        145,323               222,770               161,792
    Furniture and equipment                           58,699                50,720                57,801
    Loss on foreclosed real estate                      --                 398,681                  --
    Other non-interest expenses                      280,394               377,574               279,998
                                                  ----------            ----------            ----------

           Total non-interest expenses             1,035,229             1,559,512             1,020,697
                                                  ----------            ----------            ----------

Income before income taxes                           636,083                65,519               323,652
Income tax expense                                   288,500                51,940               138,299
                                                  ----------            ----------            ----------

NET INCOME                                        $  347,583            $   13,579            $  185,353
                                                  ==========            ==========            ==========


NET INCOME PER SHARE                              $      .48            $      .02            $      .25
                                                  ==========            ==========            ==========
</TABLE>

                                        3
<PAGE>   6
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                 CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY
               NINE MONTHS ENDED SEPTEMBER 30, 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                                      --                  --               522,692            --                522,692
                                          ------------        ------------        ------------        --------         ------------

Balance
  Sept 30, 1996                           $  1,443,840        $  4,284,804        $ 12,684,128              $-         $ 18,412,772
                                          ============        ============        ============        ========         ============


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

  Net income                                      --                  --               471,452            --                471,452

  Purchase of
         treasury stock                           --                  --                  --            (7,521)              (7,521)
                                          ------------        ------------        ------------        --------         ------------

Balance
  Sept 30, 1997                           $  1,443,840        $  4,284,804        $ 13,395,738        ($ 7,521)        $ 19,116,861
                                          ============        ============        ============        ========         ============

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

  Net income                                      --                  --             1,017,345            --              1,017,345

  Purchase of
    treasury stock                                --                  --                  --           (21,257)             (21,257)
                                          ------------        ------------        ------------        --------         ------------

Balance
  Sept 30, 1998                           $  1,443,840        $  4,284,804        $ 15,186,173        ($93,154)        $ 20,821,663
                                          ============        ============        ============        ========         ============
</TABLE>

                                        4
<PAGE>   7
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
               NINE MONTHS ENDED SEPTEMBER 30, 1998, 1996 AND 1995
                                    UNAUDITED

<TABLE>
<CAPTION>
                                                 1998                  1997                 1996
                                             ------------         ------------         ------------
<S>                                          <C>                  <C>                  <C>
OPERATING ACTIVITIES:
Net income                                   $  1,017,345         $    471,452         $    522,692
Adjustments to reconcile net
 income to cash provided by
 operating activities:
  Provision for credit losses                     225,000              435,000              350,000
    Depreciation and amortization                 102,278              104,437               86,440
    Net accretion of securities                  (195,090)             (34,642)             (58,820)
     discounts
    Loss on sale of foreclosed real
     estate                                          --               (398,681)                --
    Increase (decrease) in interest
   receivable and other assets                    (91,214)            (200,366)             276,501
    Increase (decrease) in interest
     payable and other liabilities                173,386               96,723               39,402
                                             ------------         ------------         ------------
           NET CASH PROVIDED BY
            OPERATING ACTIVITIES                1,231,705              473,923            1,216,215
                                             ------------         ------------         ------------
INVESTING ACTIVITIES:
 Net decrease in
    Federal funds sold                        (11,900,000)          (4,700,000)           2,900,000
 Proceeds from maturities of
    investment securities                      13,009,840           12,000,000            7,000,000
 Return of capital on invest-
    ment securities                               252,153            4,140,724              218,890
 Purchase of investment
  securities                                   (7,079,870)         (14,512,300)          (6,965,000)
 Net (increase) decrease in loans               2,867,735            2,132,983           (5,122,394)
 Proceeds from sale of foreclosed
    real estate                                      --              3,903,818                 --
 Capital acquisitions                            (343,984)            (171,707)            (256,400)
 Purchase of treasury stock                       (21,257)              (7,521)                --
                                             ------------         ------------         ------------
           NET CASH PROVIDED BY (USED
            IN) INVESTING ACTIVITIES           (3,215,383)           2,785,997           (2,224,904)
                                             ------------         ------------         ------------
FINANCING ACTIVITIES:
 Net increase (decrease)
     in demand deposits                          (356,946)            (199,595)             195,978
 Net increase (decrease)
     in NOW accounts                           13,280,279             (732,969)           1,270,594
 Net decrease in savings deposits                (513,804)          (1,467,173)          (1,265,929)
 Net increase (decrease) in
    time deposits                              (8,966,471)          (2,138,010)             180,457
 Net increase (decrease) in
    borrowed funds                                (88,522)             198,059              155,373
                                             ------------         ------------         ------------
           NET CASH USED BY FINANCING
            ACTIVITIES                          3,354,536           (4,339,688)             536,473
                                             ------------         ------------         ------------
Increase (decrease) in cash and
 cash equivalents                               1,370,858           (1,079,768)            (472,216)
Cash & Cash equivalents, January 1              4,933,343            9,190,838            6,348,014
                                             ------------         ------------         ------------
Cash & Cash equivalents, Sept. 30            $  6,304,201         $  8,111,070         $  5,875,798
                                             ============         ============         ============
</TABLE>

                                        5
<PAGE>   8
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                               SEPTEMBER 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>
                                                                                    SEPT 30, 1998
                                                                           BOOK VALUE             MARKET VALUE
                                                                           ----------             ------------
<S>                                                                       <C>                      <C>
           U.S. Government Agencies                                       $ 7,069,653              $ 7,604,519
           States and political subdivisions                                   14,051                   14,051
           Other securities                                                 2,049,327                2,066,550
                                                                           ----------               ----------

                                                                          $ 9,133,031              $ 9,685,120
                                                                           ==========               ==========
</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
                               SEPTEMBER 30, 1998
                                    UNAUDITED


           NOTE 3
           NET LOANS

           The composition of net loans is as follows:

<TABLE>
<CAPTION>
                                                                          SEPTEMBER 30              DECEMBER 31
                                                                             1998                      1997
                                                                           ----------               ----------
<S>                                                                       <C>                      <C>
           Commercial loans                                               $17,035,053              $19,891,202
           Real estate loans                                               32,442,379               32,467,152
           Consumer loans                                                   1,327,928                1,328,652
                                                                           ----------               ----------

                                                                           50,805,360               53,687,006
           Less:
             Allowance for credit losses                                    1,069,514                  820,254
             Unearned income                                                  122,962                  161,133
                                                                           ----------               ----------

                                                                          $49,612,884              $52,705,619
                                                                           ==========               ==========
</TABLE>

           NOTE 4
           PREMISES AND EQUIPMENT

           The major components of premises and equipment are as follows:

<TABLE>
<CAPTION>
                                                                          SEPTEMBER 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                                                1,033,007                  975,882
                                                                           ----------               ----------

                                                                          $ 1,494,034              $ 1,252,328
                                                                           ==========               ==========
</TABLE>

                                        7
<PAGE>   10
                       BRUNSWICK BANCORP AND SUBSIDIARIES
                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITIONS AND RESULTS OF OPERATIONS
                               SEPTEMBER 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 $6,000,000 and
$3,100,000, respectively. The funds made available by these decreases were
invested in Federal funds which, for the most part, explains the $11,900,000
increase in Federal funds sold.

One the liability side of the balance sheet, time deposits decreased by
$9,000,000. However, NOW accounts increased by $13,300,000, and this increase
more than offset the decrease in time deposits and resulted in an increase in
total deposits of approximately $3,400,000.

Also noteworthy is an increase of approximately $249,000 in the allowance for
credit losses which resulted mainly from $225,000 in credit loss provisions. At
September 30, 1998 the allowance for credit losses represented 2.1% of total
loans and 69% of loans past due 90 days or more and nonaccrual loans.

The results of operations for the first three quarters of 1998 compared to the
same period of 1997 show an increase in income before taxes of approximately
$883,000. Two of the components of this substantial increase are a $181,000
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.

The main reason for increased earnings is a decrease of $517,000 in non-interest
expenses which happened primarily because during 1997 a $399,000 loss resulted
from the sale of a large foreclosed property. In addition, during 1997
approximately $150,000 in expenses resulted from the complete renovation of our
branch located in downtown New Brunswick.

The Corporation's capital position continues to be one of its strong points. At
September 30, 1998 our total risk-based capital ratio was 34.5% 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
                                                                ------            -----             -----
Nine Months Ended September 30, 1998
                 Versus
Nine Months Ended September 30, 1997
------------------------------------
<S>                                                             <C>               <C>               <C>
Interest income on:
    Loans                                                       ($134)            $  12             ($122)
    Investment securities                                        (202)              (57)             (259)
    Federal funds sold                                            557                22               579
                                                                -----             -----             -----

           Total interest income                                  221               (23)              198
                                                                -----             -----             -----

Interest expense on:
    Deposits                                                       52               (35)               17
    Borrowed funds                                               --                --                --
                                                                -----             -----             -----

           Total interest expense                                  52               (35)               17
                                                                -----             -----             -----

           Net interest income                                  $ 169             $  12             $ 181
                                                                =====             =====             =====


Quarter Ended September 30, 1998
                 Versus
Quarter Ended September 30, 1997 Interest income on:
    Loans                                                       ($ 24)            $   8             ($ 16)
    Investment securities                                         (89)              (20)             (109)
    Federal funds sold                                            202              --                 202
                                                                -----             -----             -----

           Total interest income                                   89               (12)               77
                                                                -----             -----             -----

Interest expense on:
    Deposits                                                       43               (38)                5
    Borrowed funds                                                 (1)             --                  (1)
                                                                -----             -----             -----

           Total interest expense                                  42               (38)                4
                                                                -----             -----             -----

           Net interest income                                  $  47             $  26             $  73
                                                                =====             =====             =====
</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 nine month period ended September
30, 1998.
<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



       October 23, 1998                           /s/ Carmen J. Gumina
------------------------------                    ------------------------------
             Date                                 Carmen J. Gumina
                                                  President


       October 23, 1998                           /s/ Thomas Fornale
------------------------------                    ------------------------------
             Date                                 Thomas Fornale
                                                  Treasurer