<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 JUNE 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 868,108 shares of common stock ($10.00 par) outstanding as of
August 7, 1998.


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





<PAGE>   2



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



<TABLE>
<CAPTION>
                                                                                        Page
                                                                                        ----
<S>                                                                                       <C>
Part I  - Financial Information
         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                                                    7-8

Part II - Other Information
         Item 1   Legal Proceedings                                                       9
         Item 2   Changes in Securities                                                   9
         Item 3   Defaults Upon Senior Securities                                         9
         Item 4   Submission of Matters to a Vote of Security Holders                     9
         Item 5   Other Information                                                       9
         Item 6   Exhibits and Reports on Form 8-K                                        9
</TABLE>





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<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)
                                                          June 30           December 31,
                                                           1998                1997
                                                        ---------            --------
                                     ASSETS
<S>                                                      <C>                 <C>     
Cash and due from banks                                  $  4,499            $  3,977
Federal funds sold                                          2,690               2,605
Interest-bearing deposits                                       0                   0
Investment securities available for sale                   11,892              13,873
Investment securities held to maturity
  (approximate fair value of $8,124
   and $8,137)                                              8,106               8,124
Loans, less allowance for credit losses
  of $909 and $876                                         88,750              85,583
Premises and equipment                                      2,568               2,338
Accrued interest income                                       892                 990
Other Real Estate Owned                                       322                 345
Deferred income taxes                                         180                 180
Other assets                                                  896                 307
                                                         --------            --------
                                                         $120,795            $118,322
                                                         --------            --------

                      LIABILITIES AND STOCKHOLDERS' EQUITY

Deposits
  Noninterest-bearing                                    $ 13,762            $ 13,708
  Interest-bearing                                         86,026              84,854
                                                         --------            --------
                                                           99,788              98,562
Fed Funds Purchased And Repurchase Agreements               4,258               3,390
Accrued interest payable                                      400                 391
Accrued expenses                                               60                  81
Other liabilities                                             134                  43
                                                         --------            --------
                                                          104,640             102,467
                                                         --------            --------


Stockholders' equity
  Common stock, par value $10 per share
   authorized 876,000 shares, issued and
   outstanding 868,108 shares                               8,681               8,756
  Capital surplus                                           2,921               2,920
  Retained earnings                                         4,542               4,168
                                                         --------            --------
                                                           16,144              15,844
  Net unrealized gain on securities
   available for sale                                          11                  11
                                                         --------            --------
                                                           16,155              15,855
                                                         --------            --------
                                                         $120,795            $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                   For the 
                                                    three months ended         six months ended             
                                                          June 30                   June 30           Year End
                                                    -------------------       -------------------      December
                                                     1998         1997         1998         1997         1997
                                                    ------       ------       ------       ------       ------
<S>                                                 <C>          <C>          <C>          <C>          <C>   
Interest and dividend revenue
  Loans, including fees                             $1,948       $1,733       $3,876       $3,492       $7,305
  U.S. Treasury securities                             201          323          426          666        1,260
  Government Agencies Securites                         76           57          140          117          234
  Municipal Securities                                   0            2            0            4            6
  Federal funds sold                                    63           28          110           44           64
  Deposits with banks                                    0            0            0            0            1
  Equity securities                                      7            0           13            0            0
                                                    ------       ------       ------       ------       ------
          Total interest and dividend revenue        2,295        2,143        4,565        4,323        8,870
                                                    ------       ------       ------       ------       ------
Interest expense
  Deposit interest                                     941          905        1,857        1,799        3,645
          Total interest expense                       941          905        1,857        1,799        3,645
                                                    ------       ------       ------       ------       ------

          Net interest income                        1,354        1,238        2,708        2,524        5,225

Provision for credit losses                             25            5           35           28           89
                                                    ------       ------       ------       ------       ------
          Net interest income after
            provision for credit losses              1,329        1,233        2,673        2,496        5,136

Other operating revenue
  Service charges on deposit accounts                  119          110          231          210          447
  Miscellaneous revenue                                 48           80          123          119           83
                                                    ------       ------       ------       ------       ------
          Total other operating revenue                167          190          354          329          530
                                                    ------       ------       ------       ------       ------

Other expenses
  Salaries and employee benefits                       458          470          997          968        1,869
  Occupancy                                             30           27           62           65          132
  Furniture and equipment                               25           22           53           42           93
  Other operating                                      240          193          451          383          819
                                                    ------       ------       ------       ------       ------
          Total other expenses                         753          712        1,563        1,458        2,913
                                                    ------       ------       ------       ------       ------

Income before income taxes                             743          711        1,464        1,367        2,753
Income taxes                                           272          261          538          499          998
                                                    ------       ------       ------       ------       ------

Net income                                          $  471       $  450       $  926       $  868       $1,755
                                                    ------       ------       ------       ------       ------

Earnings per common share                           $ 0.54       $ 0.51       $ 1.07       $ 0.99       $ 2.00
                                                    ------       ------       ------       ------       ------
</TABLE>





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<PAGE>   5

PEOPLES BANCORP, INC. AND SUBSIDIARY
CONSOLIDATED STATEMENTS OF CASH FLOWS (UNAUDITED)

<TABLE>
<CAPTION>
                                                                                 For the Three Months Ended
                                                                                          June 30
                                                                                    1998           1997
                                                                                   -------        -------
<S>                                                                                <C>            <C>    
CASH FLOWS FROM OPERATING ACTIVITIES
  Interest received                                                                $ 4,628        $ 4,327
  Other revenue received                                                               354            297
  Cash paid for operating expenses                                                  (2,049)        (1,297)
  Interest paid                                                                     (1,848)        (1,799)
  Taxes paid                                                                          (529)          (477)
                                                                                   -------        -------
                                                                                       556          1,051
                                                                                   -------        -------
CASH FLOWS FROM INVESTING ACTIVITIES
  Cash paid for premises, equipment, intangibles,
    and construction in progress                                                      (271)          (523)
  Net customer loans repaid (advanced)                                              (3,173)        (2,355)
  Proceeds from sales and maturities of securities
    Available for sale                                                               4,000          2,004
    Held to maturity                                                                    17            128
  Investment in securities available for sale                                       (2,012)             0
  Proceeds from other real estate                                                       23             96
                                                                                   -------        -------
                                                                                    (1,416)          (650)
                                                                                   -------        -------
CASH FLOWS FROM FINANCING ACTIVITIES
  Net change in time deposits                                                         (678)          (189)
  Net change in other deposits                                                         901           (703)
  Net change in repurchase agreements                                                1,870           (441)
  Cash paid to repurchase stock, net of proceeds of sale of 40 shares                 (232)             0
  Dividends paid                                                                      (393)          (549)
                                                                                   -------        -------
                                                                                     1,468         (1,882)
                                                                                   -------        -------

NET INCREASE (DECREASE) IN CASH                                                        608         (1,481)
CASH AND EQUIVALENTS AT BEGINNING OF PERIOD                                          6,581          6,077
                                                                                   -------        -------
CASH AND EQUIVALENTS AT END OF PERIOD                                              $ 7,189        $ 4,596
                                                                                   -------        -------

RECONCILIATION OF NET INCOME TO NET CASH PROVIDED
  FROM OPERATING ACTIVITIES
  Net income                                                                       $   926        $   868
  Adjustments
    Depreciation and amortization                                                       43             48
    Provision for loan losses                                                           35             28
    Security discount accretion, net of premium
      amortization                                                                      (6)             5
    Decrease (increase) in accrued interest
      receivable and other assets                                                     (492)            17
    Increase (decrease)
      Deferred origination fees and costs, net                                         (29)           (15)
      Accrued Interest payable and other liabilities                                    79            100
                                                                                                  -------
                                                                                   $   556        $ 1,051
                                                                                   -------        -------
</TABLE>





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<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 June 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 six months ended June 30, 1998 and 1997, total comprehensive
income, net of taxes, was $926,000 and $865,000 respectively.









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<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 27.19% at June 30, 1998 as compared to 38.07% 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
six months ended June 30, 1998 and 1997 were 17.14% and 17.53%, 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 June 30, 1998, the Bank's interest rate sensitivity, as measured by
gap analysis, showed the bank was liability-sensitive with a six month
cumulative gap, as a percentage of interest-earning assets, of 93.89%. 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 six months ended June 30, 1998, was $926,000, or
$1.07 per share, compared to $868,000, or $.99 per share, for the first six
months of 1997. The primary reason net income increased is due to an increase in
net interest income. The Bank has shifted approximately $4.5 million dollars of
its securities to higher yielding loans as of June 30, 1998 compared to June 30,
1997.

        Other operating expenses have also increased $68,000 or 17.00% from
$383,000 for the first six months of 1997 to $451,000 for the first six months
ended June 30, 1998. During the first six months of 1998, the Company incurred
operating expenses of $35,000 as compared to $3,000 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 six 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 June 30, 1998. At December 31, 1997, the
allowance was also 1.01% of gross loans. At June 30, 1998, there were two
nonaccruing mortgage loans totaling $388,000 and only 1.17% of the portfolio was
delinquent ninety days or more including nonaccruing loans.

        The Bank employed sixty one full time equivalent employees during the
second 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 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 ("Year 2000"). 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 Year 2000 compliant. Management expects no significant costs to get its
systems Year 2000 compliant. 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. 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.





                                      -8-
<PAGE>   9



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 5,805 shares of
           stock were purchased.

Item 3     Defaults Upon Senior Securities
           Not applicable

Item 4     Submission of Matters to a Vote of Security Holders

                   At the Company's Annual Meeting held on April 29, 1998,
           shareholders of the Company adopted two amendments to the Articles of
           Incorporation designed to have anti-takeover effects. The first
           amendment added a new Article Seventh to the consolidation, reverse
           stock split, sale, exchange, lease of all or substantially all of the
           assets of the Company or any similar transaction requires the
           affirmative vote of seventy-five percent (75%) of the outstanding
           shares of the Company if the transaction has not been recommended to
           shareholders by at least a majority of the Board of Directors. Any
           such transaction recommended to shareholders by a majority of the
           Board of Directors shall only be subject to the vote otherwise
           required under Maryland Law.

                   The second amendment made to the Articles of Incorporation
           was the adoption of a new Article Eighth. This provision allows the
           Board of Directors to consider a number of different factors, other
           than just price, in making any recommendation to shareholders on a
           transaction as described in Article Seventh. This provision also
           allows the Board of Directors to take a number of different actions
           if it determines that an offer should be rejected, in order to
           further prevent the possibility of an unwanted takeover offer.

                   The slate of directors proposed in the Proxy Statement dated
           April 9, 1998 were elected at the annual stockholders meeting held on
           April 29, 1998.

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.
           27  Financial Data Schedule

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





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<PAGE>   10




                                   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: July 12, 1998                   By: /s/ E. ROY OWNENS
     -------------------                  --------------------------------------
                                          E. Roy Owens
                                          President and CEO



Date: July 12, 1998                   By: /s/ THOMAS G. STEVENSON
     -------------------                  --------------------------------------
                                          Thomas G. Stevenson
                                          Executive Vice President
                                          Chief Financial Officer






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