<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                   FORM 10-QSB

(Mark One)

[X]      QUARTERLY REPORT UNDER SECTION 13 OR 15 (d) OF THE SECURITIES EXCHANGE
         ACT OF 1934 FOR THE QUARTER ENDED SEPTEMBER 30, 1998

[ ]      TRANSITION REPORT UNDER SECTION 13 OR 15(d) OF THE SECURITIES AND
         EXCHANGE ACT OF 1934 FOR THE TRANSITION PERIOD FROM __________________
         TO _________________

                       Commission File Number: 0001060244

                              PEOPLES BANCORP, INC.
               (Exact name of issuer as specified in its charter)

          Maryland                                        52-2027776            
------------------------                    ------------------------------------
(State of incorporation)                    (I.R.S. Employer Identification No.)

          P. O. Box 210, 100 Spring Street, Chestertown, Maryland 21620
--------------------------------------------------------------------------------
                     (Address of principal executive offices

                                 (410) 778-3500
--------------------------------------------------------------------------------
                           (Issuer's telephone number)

                                 Not Applicable
--------------------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                         if changed since last report)


Check whether the issuer (1) filed all reports required to be filed by Section
13 or 15(d) of the Exchange Act during the past 12 months (or for such shorter
period that the registrant was required to file such reports), and (2) has been
subject to such filing requirements for the past 90 days. 
YES  X      NO 
   ------      -------

State the number of shares outstanding of each of the issuer's classes of common
equity, as of the latest practicable date:

The registrant has 858,208 shares of common stock ($10.00 par) outstanding as of
November 10, 1998.


Transitional Small Business Disclosure Format (check one) YES       NO    X  
                                                              -----    ------

PEOPLES BANCORP, INC. AND SUBSIDIARY
FORM 10-QSB
INDEX


<PAGE>   2


<TABLE>
<S>                                                                                     <C>
Part I - Financial Information                                                                 Page

         Item 1   Financial Statements
                  Consolidated Statements of Condition                                           3
                  Consolidated Statements of Income                                              4
                  Consolidated Statements of Cash Flows                                          5
                  Notes to Financial Statements                                                  6

         Item 2   Management's Discussion and Analysis of Financial Condition
                  and Results of Operation                                                     7-9

Part II - Other Information

         Item 1   Legal Proceedings                                                              10
         Item 2   Changes in Securities                                                          10
         Item 3   Defaults Upon Senior Securities                                                10
         Item 4   Submission of Matters to a Vote of Security Holders                            10
         Item 5   Other Information                                                              10
         Item 6   Exhibits and Reports on Form 8-K                                               10
</TABLE>







                                      -2-
<PAGE>   3



PEOPLES BANCORP, INC. AND SUBSIDIARY

PART I - FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS

CONSOLIDATED STATEMENTS OF CONDITION

                               (DOLLAR AMOUNTS IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                                 (unaudited)
                                                                                September 30          December 31,
                                                                                    1998                1997
                                                                                  --------            --------
<S>                                                                               <C>                 <C>     
                                                 ASSETS
Cash and due from banks                                                           $  3,458            $  3,977
Federal funds sold                                                                   4,658               2,605
Interest-bearing deposits                                                                0                   0
Investment securities available for sale                                            12,030              13,873
Investment securities held to maturity
  (approximate fair value of $6,667
   and $8,137)                                                                       6,599               8,124
Loans, less allowance for credit losses
  of $924 and $876                                                                  90,266              85,583
Premises and equipment                                                               2,684               2,063
Accrued interest income                                                                899                 990
Other Real Estate Owned                                                                137                 345
Deferred income taxes                                                                  144                 180
Other assets                                                                           194                 582
                                                                                  --------            --------
                                                                                  $121,069            $118,322
                                                                                  --------            --------

                                  LIABILITIES AND STOCKHOLDERS' EQUITY
Deposits
  Noninterest-bearing                                                             $ 12,871            $ 13,708
  Interest-bearing                                                                  86,403              84,854
                                                                                  --------            --------
                                                                                    99,274              98,562
Fed Funds Purchased And Repurchase Agreements                                        4,945               3,390
Accrued interest payable                                                               413                 391
Accrued expenses                                                                       214                  81
Other liabilities                                                                       84                  43
                                                                                  --------            --------
                                                                                   104,930             102,467
                                                                                  --------            --------
Stockholders' equity
  Common stock, par value $10 per share
   authorized 876,000 shares, issued and
   outstanding 858,208 shares                                                        8,582               8,756
  Capital surplus                                                                    2,921               2,920
  Retained earnings                                                                  4,568               4,168
                                                                                  --------            --------
                                                                                    16,071              15,844
  Net unrealized gain on securities
   available for sale                                                                   68                  11
                                                                                  --------            --------
                                                                                    16,139              15,855
                                                                                  --------            --------
                                                                                  $121,069            $118,322
                                                                                  --------            --------
</TABLE>





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<PAGE>   4


PEOPLES BANCORP, INC. AND SUBSIDIARY

CONSOLIDATED STATEMENTS OF INCOME (UNAUDITED)

(DOLLAR AMOUNTS IN THOUSANDS EXCEPT PER-SHARE DATA)

<TABLE>
<CAPTION>
                                                   For the three months ended    For the nine months ended      Year End
                                                          September 30                   September 30           December
                                                      ---------------------         ---------------------       --------
                                                       1998           1997           1998           1997          1997
                                                      ------         ------         ------         ------        ------
<S>                                                   <C>            <C>            <C>            <C>           <C>   
Interest and dividend revenue
  Loans, including fees                               $1,957         $1,838         $5,833         $5,330         $7,305
  U.S. Treasury securities                               201            315            627            981          1,260
  Government Agencies Securities                          71             59            211            176            234
  Municipal Securities                                     0              1              0              5              6
  Federal funds sold                                      88             10            198             54             64
  Deposits with banks                                      0              0              0              0              1
  Equity securities                                        6              0             19              0              0
                                                      ------         ------         ------         ------         ------
          Total interest and dividend revenue          2,323          2,223          6,888          6,546          8,870
                                                      ------         ------         ------         ------         ------
Interest expense
  Deposit and Repurchase Agreement                       971            928          2,828          2,727          3,645
          Total interest expense                         971            928          2,828          2,727          3,645
                                                      ------         ------         ------         ------         ------
          Net interest income                          1,352          1,295          4,060          3,819          5,225
Provision for credit losses                               14             26             49             54             89
                                                      ------         ------         ------         ------         ------
          Net interest income after
            provision for credit losses                1,338          1,269          4,011          3,765          5,136
Other operating revenue
  Service charges on deposit accounts                    128            117            359            327            447
  Miscellaneous revenue                                   42             47            165            166             83
                                                      ------         ------         ------         ------         ------
          Total other operating revenue                  170            164            524            493            530
                                                      ------         ------         ------         ------         ------
Other expenses
  Salaries and employee benefits                         506            468          1,503          1,436          1,869
  Occupancy                                               34             34             96             99            132
  Furniture and equipment                                 31             23             84             65             93
  Other operating                                        212            226            663            609            819
                                                      ------         ------         ------         ------         ------
          Total other expenses                           783            751          2,346          2,209          2,913
                                                      ------         ------         ------         ------         ------
Income before income taxes                               725            682          2,189          2,049          2,753
Income taxes                                             273            260            811            759            998
                                                      ------         ------         ------         ------         ------
Net income                                            $  452         $  422         $1,378         $1,290         $1,755
                                                      ------         ------         ------         ------         ------
Basic earnings per common share                       $ 0.52         $ 0.48         $ 1.58         $ 1.47         $ 2.00
                                                      ------         ------         ------         ------         ------
</TABLE>







                                      -4-
<PAGE>   5



PEOPLES BANCORP, INC. AND SUBSIDIARY

CONSOLIDATED STATEMENTS OF CASH FLOWS (UNAUDITED)

<TABLE>
<CAPTION>
                                                                             For the Nine Months Ended
                                                                                    September 30
                                                                               1998             1997
                                                                              -------          -------
<S>                                                                           <C>              <C>    
CASH FLOWS FROM OPERATING ACTIVITIES
  Interest received                                                           $ 6,961          $ 6,658
  Other revenue received                                                          603              374
  Cash paid for operating expenses                                             (2,231)          (1,907)
  Interest paid                                                                (2,806)          (2,716)
  Taxes paid                                                                     (633)            (787)
                                                                              -------          -------
                                                                                1,894            1,622
                                                                              -------          -------
CASH FLOWS FROM INVESTING ACTIVITIES
  Cash paid for premises, equipment, intangibles,
    and construction in progress                                                 (411)            (986)
  Net customer loans repaid (advanced)                                         (4,704)          (5,044)
  Proceeds from sales and maturities of securities
    Available for sale                                                          6,997            5,005
    Held to maturity                                                            1,527              152
  Investment in securities available for sale                                  (5,073)            (343)
  Proceeds from other real estate                                                 189               96
                                                                              -------          -------
                                                                               (1,475)          (1,120)
                                                                              -------          -------

CASH FLOWS FROM FINANCING ACTIVITIES
  Net change in time deposits                                                     (60)             958
  Net change in other deposits                                                   (231)          (2,385)
  Net change in repurchase agreements                                           2,557             (308)
  Cash paid to repurchase stock, net of proceeds of sale of 40 shares            (549)               0
  Dividends paid                                                                 (601)            (926)
                                                                              -------          -------
                                                                                1,116           (2,661)
                                                                              -------          -------
NET INCREASE (DECREASE) IN CASH                                                 1,535           (2,159)
CASH AND EQUIVALENTS AT BEGINNING OF PERIOD                                     6,581            6,077
                                                                              -------          -------
CASH AND EQUIVALENTS AT END OF PERIOD                                         $ 8,116          $ 3,918
                                                                              -------          -------
RECONCILIATION OF NET INCOME TO NET CASH PROVIDED
  FROM OPERATING ACTIVITIES
  Net income                                                                  $ 1,378          $ 1,290
  Adjustments
    Depreciation and amortization                                                  77               77
    Provision for loan losses                                                      49               54
    Security discount accretion, net of premium
      amortization                                                                 10               10
    Loss (gains) on sales                                                          19               -2
    Decrease (increase) in accrued interest
      receivable and other assets                                                 193              100
    Increase (decrease)
      Deferred origination fees and costs, net                                    (28)             (23)
      Accrued Interest payable and other liabilities                              196              116
                                                                              -------          -------
                                                                              $ 1,894          $ 1,622
                                                                              -------          -------
</TABLE>







                                      -5-
<PAGE>   6


PEOPLES BANCORP, INC. AND SUBSIDIARY
NOTES TO FINANCIAL STATEMENTS


1.       Basis of Presentation

                  The accompanying unaudited condensed financial statements have
         been prepared in accordance with generally accepted accounting
         principles for the interim financial information and with the
         instructions to Form 10-QSB and Regulation S-X of the Securities and
         Exchange Commission. Accordingly, they do not include all the
         information and footnotes required by generally accepted accounting
         principles for complete financial statements. In the opinion of
         management, all adjustments (consisting of normal recurring accruals)
         considered necessary for a fair presentation have been included.
         Operating results of the quarters ended September 30, 1998 and 1997 are
         not necessarily indicative of the results that may be expected for the
         years ending December 31, 1998 and 1997. For further information, refer
         to the financial statements and footnotes included in the registration
         statement dated May 1, 1998.

2.       Cash Flows

                  For purposes of reporting cash flows, cash and cash
         equivalents include cash on hand, amounts due from banks and overnight
         investments in federal funds sold.

3.       Comprehensive income

                  Effective January 1, 1998, the Company adopted Statement of
         Financial Accounting Standards (FAS) No., 130, Reporting Comprehensive
         Income. SFAS No. 130 requires the reporting of comprehensive income
         which includes unrealized gains and losses not recognized in net
         income. Unrealized gains and losses on available-for-sale securities
         which have been reported as a separate component of stockholders'
         equity are included in comprehensive income. The adoption of SFAS No.
         130 had no impact on the Company's net income or stockholders' equity.

                  For the nine months ended September 30, 1998 and 1997, total
         comprehensive income, net of taxes, was $1,435,000 and $1,314,000
         respectively.









                                      -6-
<PAGE>   7


PEOPLES BANCORP, INC. AND SUBSIDIARY
PART I FINANCIAL INFORMATION
ITEM 2   MANAGEMENT'S DISCUSSION AND ANALYSIS OR PLAN OF OPERATION.

            This Report contains statements which constitute forward-looking
statements within the meaning of Section 27A of the Securities Act of 1933 and
Section 21E of the Securities Exchange Act of 1934. These statements appear in a
number of places in this Report and include all statements regarding the intent,
belief or current expectations of the Company, its directors or its officers
with respect to, among other things: (i) the Company's financing plans; (ii)
trends affecting the Company's financial condition or results of operations;
(iii) the Company's growth strategy and operating strategy; and (iv) the
declaration and payment of dividends. Investors are cautioned that any such
forward-looking statements are not guarantees of future performance and involve
risks and uncertainties, and that actual results may differ materially from
those projected in the forward-looking statements as a result of various factors
discussed herein and those factors discussed in detail in the Company's filings
with the Securities and Exchange Commission.

        The following discussion of the financial condition and results of
operations of the Registrant (the Company) should be read in conjunction with
the Company's financial statements and related notes and other statistical
information included elsewhere herein.

General

        The Company was incorporated in Maryland on December 10, 1996 as a bank
holding company. Stock of a Maryland state bank with the name Peoples Bank of
Kent County, Maryland (the "Bank") was exchanged in March, 1997 for the
outstanding stock of the Company.

        The Bank was established and incorporated in 1910. The Company currently
engages in no business other than owning and managing the Bank.

Financial Condition, Liquidity and Sources of Capital

        The primary sources of liquidity of the Bank are from loan payments,
short-term investments, including federal funds sold, and cash and due from
banks. Average liquid assets (cash and amounts due from banks, interest bearing
deposits in other banks, federal funds sold, and investment securities) compared
to average deposits were 30.82% at September 30, 1998 as compared to 33.52% at
the same period last year. Another source of liquidity is a secured line of
credit for $15,000,000 from the Federal Home Loan Bank as well as lines of
credit in the amount of $6,000,000 from correspondent banks, namely, NationsBank
and First National Bank of Maryland.

        Tier one capital ratios of the Bank, based on average assets for the
nine months ended September 30, 1998 and 1997 were 16.74% and 17.72%,
respectively. Both are substantially in excess of regulatory minimum
requirements. The Bank expects that its current capital and short-term
investments will satisfy the Bank's cash requirements for the foreseeable
future. However, no assurance can be given in this regard as rapid growth,
deterioration in loan quality or a downturn in earnings, or a combination of
these factors could change the Bank's capital position in a relatively short
period of time.

        At September 30, 1998, the Bank's interest rate sensitivity, as measured
by gap analysis, showed the bank was liability-sensitive with a nine month
cumulative gap, as a percentage of interest-earning assets, of 86.86%. This
shows that the bank is fairly evenly matched where any rate change will affect
the same amount of both assets and liabilities. Generally, liability sensitivity
indicates that a higher dollar amount of liabilities re-price than assets and in
a declining rate environment net interest income increases. On the other hand,
if interest rates increase, then typically the net interest income should
decline. The bank controls this matching of assets to liabilities to minimize
interest rate risk while at the same time maximizing income.






                                      -7-
<PAGE>   8


Results and Plan of Operation

        Net income for the nine months ended September 30, 1998, was $1,378,000,
or $1.58 per share, compared to $1,290,000, or $1.47 per share, for the first
nine months of 1997. The primary reason net income increased is due to an
increase in net interest income. The Bank has shifted approximately $5.5 million
dollars of its securities to higher yielding loans as of September 30, 1998
compared to September 30, 1997.

        Other operating expenses have also increased $54,000 or 8.87% from
$609,000 for the first nine months of 1997 to $663,000 for the first nine months
ended September 30, 1998. During the first nine months of 1998, the Company
incurred operating expenses of $46,000 as compared to $35,000 for the same
period in 1997, primarily due to costs associated with the initial filing
requirements with regulatory authorities and other initial ancillary costs. In
addition, the Bank incurred a nonrecurring type of expense of $19,000 in the
first nine months of 1998 on a foreclosed property because of unexpected
improvements that had to be made to help make the property marketable.

        The Bank reviewed its loan portfolio and determined the allowance, at
1.01% of gross loans, was adequate at September 30, 1998. At December 31, 1997,
the allowance was also 1.01% of gross loans. At September 30, 1998, there were
three nonaccruing mortgage loans totaling $416,000 and only 1.41% of the
portfolio was delinquent ninety days or more including nonaccruing loans.

        The Bank employed sixty one full time equivalent employees during the
third quarter of 1998. The Company employs no employees outside those hired by
the Bank.

        The Bank offers a variety of commercial banking services in its trade
area, which encompasses all of Kent County, northern Queen Anne's County and
southern Cecil County, Maryland. This primary service area is located between
the Chesapeake Bay and the western boundary of Delaware. The Bank emphasizes its
primary goal of meeting the banking needs of individuals and small to medium
sized business in its daily operations. The Bank offers a full range of deposit
services that are generally available in most banks and other similar
institutions, i.e., checking accounts, now accounts, savings accounts and other
time deposits of various types, ranging from daily money market accounts to
long-term certificates of deposit.

        The Bank also offers a broad range of short and medium term commercial
and personal loans. The bank originates demand and balloon type mortgage loans
to fit may types of loan requests, i.e., real estate construction, acquisition,
home equity and a variety of commercial purposes. Loans originated to date are
anticipated to be held in the Bank's portfolio.

        The Bank's services also include cash management opportunities, safe
deposit boxes, direct deposit of various types of needs, automatic transfers of
funds, as well as discount brokerage services and financial planning, along with
security sales and purchases, including mutual funds and annuities. The bank
also offers ATM services though the Most and Cirrus networks. The Bank offers
Master Card and Visa credit card services through a correspondent bank as an
agent for the Bank as well as debit card services.

Year 2000 Issues

        The year 2000 (Y2K) presents many potential problems for businesses and
individuals. In an effort to conserve hard drive space, programers wrote
programs that would not recognize the year 2000 correctly. This can cause system
failures for computers and other electronic equipment that have chip components.
Management has a Y2K committee, which reports to the Board responsible for
assessing progress in the Company's plans to minimize the effects of the Y2K
problem.

        The Company uses a third-party data processor for most of its accounting
functions. The processor has implemented many changes in preparation for the
year 2000 (Y2K). Testing should be complete by the end of 1998. The Company also
has a number of portable computers, most of which, due to their age, are Y2K
compliant. Management expects no significant additional costs to get its systems
Y2K compliant.





                                      -8-
<PAGE>   9


        The largest Year 2000 exposure to most banks is the preparedness of the
customers of the banks. Management is addressing with its customers the possible
consequences of not being prepared for Year 2000. Statement enclosures have are
being mailed to every customer. Should large borrowers not sufficiently address
this issue, the Company may experience an increase in loan defaults. The amount
of potential loss from this issue is not quantifiable. Management is attempting
to reduce this exposure by educating its customers. The Company's adopted a
Comprehensive Plan that has budgeted $12,500 to cover century date projects. Of
this budgeted amount, management has used $1,663.

Market Risk

        Net interest income of the Company is one of the most important factors
in evaluating the financial performance of the Company. The Company uses
interest sensitivity analysis to determine the effect of rate changes. Net
interest income is projected over the one-year period to determine the effect of
an increase or decrease in the prime rate of 100 basis points. If prime were to
decrease 100 basis points, the Company would experience a decrease in net
interest income of $464, if all assets and liabilities maturing within that
period were adjusted for the rate change. The sensitivity analysis does not
consider the likelihood of these rate changes nor whether management's reaction
to this rate change would be to reprice its loans and deposits. This paragraph
contains certain forward-looking statements within the meaning of and made
pursuant to the safe harbor provisions of the Private Litigation Securities
Reform Act of 1995.

















                                      -9-
<PAGE>   10


PEOPLES BANCORP, INC. AND SUBSIDIARY
PART II OTHER INFORMATION


Item 1               Legal Proceedings
                     -----------------
                     Not applicable

Item 2               Changes in Securities
                     ---------------------
                     The Bank adopted a policy of purchasing stock from existing
                     stockholders. During the present quarter 9,900 shares of
                     stock were purchased.

Item 3               Defaults Upon Senior Securities
                     -------------------------------
                     Not applicable

Item 4               Submission of Matters to a Vote of Security Holders
                     ---------------------------------------------------
                     Not applicable

Item 5               Other information
                     -----------------
                     Not applicable.

Item 6               Exhibits and Reports on Form 8-K
                     --------------------------------
              a)     Exhibits
                           1. Proxy Statement dated April 9, 1998, is
                           incorporated by reference.
                           2. Registration statement dated May 1, 1998, is
                           incorporated by reference.

              b)     Reports on Form 8-K
                     There were no reports on Form 8-K filed for the quarter
                     ended September 30, 1998.







                                      -10-
<PAGE>   11


                                   SIGNATURES

             Pursuant to the requirements of Section 13 or 15(d) of the
Securities Exchange Act of 1934, the Registrant has duly caused this report to
be signed on its behalf by the undersigned, thereunto duly authorized.



                                        PEOPLES BANCORP, INC. 







Date:  November 13, 1998                By:  /s/ E. Roy Owens
                                             -----------------------------------
                                             E. Roy Owens
                                             President and CEO



Date:  November 13, 1998                By:  /s/ Thomas G. Stevenson
                                             -----------------------------------
                                             Thomas G. Stevenson
                                             Executive Vice President
                                             Chief Financial Officer











                                      -11-