<PAGE>   1
 
================================================================================
 
                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                            ------------------------
 
                                   FORM 10-Q
 
[X]         QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
      SECURITIES EXCHANGE ACT OF 1934 FOR THE PERIOD ENDED MARCH 31, 1998
 
                                       OR
 
[ ]         TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
 SECURITIES EXCHANGE ACT OF 1934 FOR THE TRANSITION PERIOD FROM              TO
 
COMMISSION FILE NUMBER 33-89506
 
                        BERTHEL GROWTH & INCOME TRUST I
             (Exact name of Registrant as specified in its charter)
 
                                    DELAWARE
                        (State or other jurisdiction of
                         incorporation or organization)
                                   52-1915821
                                (I.R.S. Employer
                              Identification No.)
 
                    100 SECOND STREET SE, CEDAR RAPIDS, IOWA
                    (Address of principal executive offices)
                                     52401
                                   (Zip Code)
 
                                 (319) 365-2506
              Registrant's telephone number, including area code:
 
     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 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           No  _
 
                      Applicable Only to Corporate Issuers
 
     Indicate the number of shares outstanding of each of the issuer's classes
of common stock, as of the latest practical date.
 
      Shares of Beneficial Interest -- 10,541 shares as of April 30, 1998
 
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<PAGE>   2
 
                        BERTHEL GROWTH & INCOME TRUST I
 
                                     INDEX
 
PART I. FINANCIAL INFORMATION
ITEM 1.      FINANCIAL STATEMENTS (UNAUDITED):
             CONSOLIDATED STATEMENTS OF ASSETS AND LIABILITIES -- MARCH 31, 
             1998 AND DECEMBER 31, 1997
             CONSOLIDATED STATEMENTS OF OPERATIONS -- THREE MONTHS ENDED MARCH 
             31, 1998 AND MARCH 31, 1997
             CONSOLIDATED STATEMENTS OF CHANGES IN NET ASSETS -- THREE MONTHS 
             ENDED MARCH 31, 1998 AND MARCH 31, 1997
             CONSOLIDATED STATEMENTS OF CASH FLOWS -- THREE MONTHS ENDED MARCH 
             31, 1998 AND MARCH 31, 1997 NOTES TO THE FINANCIAL STATEMENTS
ITEM 2.      MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
             RESULTS OF OPERATIONS
PART II. OTHER INFORMATION
Item 1.      Legal proceedings -- none
Item 2.      Changes in securities -- none
Item 3.      Defaults upon senior securities -- none
Item 4.      Submission of matters to a vote of shareholders -- none
Item 5.      Other information -- none
Item 6.      Exhibits and reports on Form 8-K
             a. Exhibits -- none
             b. No report on Form 8-K was filed for the quarter ended March 31,
                1998
Signatures
 
                                        2
<PAGE>   3
 
                        BERTHEL GROWTH & INCOME TRUST I
 
         CONSOLIDATED STATEMENTS OF ASSETS AND LIABILITIES (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                MARCH 31, 1998    DECEMBER 31, 1997
                                                                --------------    -----------------
<S>                                                             <C>               <C>
ASSETS
Investments in securities (Note B)..........................      $2,800,000         $2,800,000
Cash........................................................          15,912             15,047
Temporary investment in money market securities.............       4,493,747          4,587,598
Interest receivable.........................................          29,167              5,833
Other assets................................................          56,302             53,475
                                                                  ----------         ----------
     Total Assets...........................................       7,395,128          7,461,953
                                                                  ----------         ----------
LIABILITIES
Accounts payable and other accrued expenses.................          16,484             36,509
Distributions payable to shareholders.......................         881,883            818,689
Due to affiliate............................................          45,780             15,797
                                                                  ----------         ----------
     Total Liabilities......................................         944,147            870,995
                                                                  ----------         ----------
COMMITMENTS AND CONTINGENCIES
Net Assets (equivalent to $611.99 per share in 1998 and
  $625.27 per share in 1997)................................      $6,450,981         $6,590,958
                                                                  ==========         ==========
Net assets consist of:
  Shares of beneficial interest (25,000 shares authorized;
     10,541 shares issued and outstanding...................      $7,110,135         $7,318,066
  Undistributed net investment loss.........................        (659,154)          (727,108)
                                                                  ----------         ----------
                                                                  $6,450,981         $6,590,958
                                                                  ==========         ==========
</TABLE>
 
                       See notes to financial statements.
 
                                        3
<PAGE>   4
 
                        BERTHEL GROWTH & INCOME TRUST I
 
               CONSOLIDATED STATEMENTS OF OPERATIONS (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                       THREE MONTHS ENDED
                                                                --------------------------------
                                                                MARCH 31, 1998    MARCH 31, 1997
                                                                --------------    --------------
<S>                                                             <C>               <C>
REVENUES:
  Interest income...........................................       $143,147          $104,693
  Other income..............................................          2,500               500
                                                                   --------          --------
                                                                    145,647           105,193
                                                                   --------          --------
EXPENSES:
  Management fees...........................................         45,780            41,473
  Administrative services...................................          9,754             9,754
  Trustee fees..............................................          8,000             6,000
  Auditing and accounting fees..............................          4,917             4,225
  Legal expense.............................................          4,328            14,840
  Other general and administrative expenses.................          4,914             3,443
                                                                   --------          --------
  Total expenses............................................         77,693            79,735
                                                                   --------          --------
Net investment income and net increase in net assets
  resulting from operations.................................       $ 67,954          $ 25,458
                                                                   ========          ========
Net investment income per beneficial share..................       $   6.45          $   2.82
                                                                   ========          ========
Weighted average shares.....................................         10,541             9,038
</TABLE>
 
                       See notes to financial statements.
 
                                        4
<PAGE>   5
 
                        BERTHEL GROWTH & INCOME TRUST I
 
          CONSOLIDATED STATEMENTS OF CHANGES IN NET ASSETS (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                          THREE MONTHS ENDED          THREE MONTHS ENDED
                                                            MARCH 31, 1998              MARCH 31, 1997
                                                       ------------------------    ------------------------
                                                       SHARES OF                   SHARES OF
                                                       BENEFICIAL                  BENEFICIAL
                                                        INTEREST       AMOUNT       INTEREST       AMOUNT
                                                       ----------      ------      ----------      ------
<S>                                                    <C>           <C>           <C>           <C>
Net investment income..............................          --      $   67,954         --       $   25,458
                                                                     ----------                  ----------
Net increase in assets resulting from operations...          --          67,954                      25,458
Proceeds from sales of Shares of beneficial
  interest.........................................          --             -0-        294          294,000
Syndication costs incurred.........................          --             -0-         --          (42,492)
Shares of beneficial interest redeemed.............          --             -0-         (5)          (5,000)
Distributions payable to shareholders..............          --        (207,931)        --         (220,741)
Net assets at beginning of period..................      10,541       6,590,958      8,891        5,887,979
                                                         ------      ----------      -----       ----------
Net assets at end of period........................      10,541      $6,450,981      9,180       $5,939,204
                                                         ======      ==========      =====       ==========
</TABLE>
 
                       See notes to financial statements.
 
                                        5
<PAGE>   6
 
                        BERTHEL GROWTH & INCOME TRUST I
 
                CONSOLIDATED STATEMENT OF CASH FLOWS (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                             THREE MONTHS ENDED    THREE MONTHS ENDED
                                                               MARCH 31, 1998        MARCH 31, 1997
                                                             ------------------    ------------------
<S>                                                          <C>                   <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net investment income..................................        $  67,954             $  25,458
  Adjustments to reconcile net investment loss to net
     cash flows from operating activities:
     Amortization of organizational costs................              250                   250
     Gain on redemption of unit..........................              -0-                  (500)
     Changes in operating assets and liabilities:
       Temporary investment in money market securities...           93,851              (609,409)
       Other assets......................................           (3,077)               (3,168)
       Interest receivable...............................          (23,334)                3,954
       Due to affiliate..................................           29,983                (5,549)
       Accounts payable and accrued expenses.............          (20,025)               (6,253)
                                                                 ---------             ---------
          Net cash flows from operating activities.......          145,602              (595,217)
                                                                 ---------             ---------
CASH FLOWS FROM INVESTING ACTIVITIES:
  Repayment of note receivable...........................              -0-               275,304
CASH FLOWS FROM FINANCING ACTIVITIES:
  Distribution payments to Shareholders..................         (144,737)                  -0-
  Proceeds from sales of shares of beneficial interest...              -0-               294,000
  Redemption of shares of beneficial interest............              -0-                (4,500)
  Syndication costs incurred.............................              -0-               (42,492)
                                                                 ---------             ---------
          Net cash flows from financing activities.......         (144,737)              247,008
                                                                 ---------             ---------
Net Increase (Decrease) in Cash..........................              865               (72,905)
Cash at Beginning of Period..............................           15,047                97,025
                                                                 ---------             ---------
Cash at End of Period....................................        $  15,912             $  24,120
                                                                 =========             =========
SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:
  Noncash financing activities:
     Distributions payable to shareholders...............        $ 207,931             $ 220,741
</TABLE>
 
                       See notes to financial statements.
 
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<PAGE>   7
 
                        BERTHEL GROWTH & INCOME TRUST I
                   NOTES TO FINANCIAL STATEMENTS (UNAUDITED)
 
NOTE A -- BASIS OF PRESENTATION
 
     The accompanying unaudited 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 Article 10 of Regulation
S-X. Accordingly, they do not include all information and footnotes required by
generally accepted accounting principles for complete financial statements and
should be read in conjunction with the Company's Form 10-K filed with the
Securities and Exchange Commission for the year ended December 31, 1997. In the
opinion of management, all adjustments (consisting of normal recurring accruals)
considered necessary for a fair representation have been included. Operating
results for the three months ended March 31, 1998 are not necessarily indicative
of the results that may be expected for the year ended December 31, 1998.
 
     The preparation of the Company's financial statements in conformity with
generally accepted accounting principles necessarily requires management to make
estimates and assumptions that affect the reported amounts of assets and
liabilities and disclosure of contingent assets and liabilities at the date of
financial statements and the reported amounts of revenues and expenses during
the reporting period. Actual results could differ from those estimates.
 
NOTE B -- INVESTMENTS
 
<TABLE>
<CAPTION>
                                                             COST       VALUATION
                                                             ----       ---------
<S>                                                       <C>           <C>
VisionComm, Inc.:
  Note receivable.....................................    $  500,000    $  500,000
  Warrants for 125,000 shares at $5/share.............           -0-           -0-
  Warrants for 17,590 shares at $5/share..............           -0-           -0-
Soil Recovery Services, Inc.:
  Convertible subordinated debenture..................     1,000,000           -0-
Kinseth Hospitality Company, Inc.:
  Note receivable.....................................     2,000,000     2,000,000
  Warrants for 25% of the outstanding common stock at
     $0.01 per share..................................           -0-           -0-
LIVEware5, Inc.:
  300,000 shares of common stock, no par value and
     warrants for 600,000 shares at $0.01 per share...       300,000       300,000
                                                          ----------    ----------
                                                          $3,800,000    $2,800,000
                                                          ==========    ==========
</TABLE>
 
     On April 30, 1996, the Trust made a commitment to invest up to $2,180,000
in VisionComm, Inc. ("VisionComm"), which is primarily engaged in the
telecommunications and private cable television business. This investment was in
the form of a 14%; five-year secured note with a seven year warrant for 125,000
shares of common stock exercisable until April 30, 2003 at an exercise price of
$5 per share. VisionComm repaid 100% of the outstanding balance during 1997.
 
     On December 1, 1997, the Trust provided an additional $500,000 in financing
to VisionComm in the form of a 14%; 12-month secured note with warrants. This
note is secured by all the private cable assets of VisionComm. The warrants
received have terms equivalent to those received in conjunction with the Trust's
previous investment in VisionComm with the exception that all warrants now owned
by the Trust provide for the option of a cashless exercise. The warrants
received with this round of financing are for 17,590 shares of common stock
exercisable until April 30, 2003 at an exercise price of $5 per share.
 
     The Trust now has the right through this latter warrant and the other
warrants it previously owned to purchase approximately 24% of the equity
ownership of VisionComm. This right expires on April 30, 2003.
 
                                        7
<PAGE>   8
                        BERTHEL GROWTH & INCOME TRUST I
            NOTES TO FINANCIAL STATEMENTS (UNAUDITED) -- (CONTINUED)
 
     The Trust has also invested $1,000,000 in a convertible subordinated
debenture issued by Soil Recovery Services, Inc. ("SRS"). The debenture is for a
seven year term with an annual interest rate of 15% with no prepayment penalty.
Interest only is due the first two years with equal principal payments due at
the end of years three through seven. The debenture can be converted at any time
at a conversion rate that will provide the Trust with approximately 21.5% of
common stock of SRS.
 
     The Trust served a Notice of Default and a Notice of Recession on SRS and
commenced litigation against key parties. The last interest payment received by
the Trust was in July 1996. SRS filed for Chapter 11 bankruptcy protection on
December 12, 1996. The Trust is continuing its avenues of recovery through the
bankruptcy court and litigation but for the year ended December 31, 1996, the
Trust recognized an unrealized loss of $1,000,000.
 
     The Trust has invested in a senior secured note issued by Kinseth
Hospitality Company, Inc. ("Kinseth"), which is primarily engaged in the
hospitality industry. The six year note carries a 14% interest rate with
interest only payments with a balloon payment due May 16, 2003. The Trust
received a warrant to purchase 25% of Kinseth's common stock for $11.80. The
warrant expires at the end of 2001. The warrant shares can by "put" to Kinseth
beginning in 2002 at a designated multiple or based on independent valuations.
Beginning in 2004, the warrant shares may be called by Kinseth at a designated
multiple or based on independent valuations.
 
     The Trust has invested $300,000 in LIVEware5, Inc. ("LIVEware"). LIVEware
is a provider of distance based corporate education via advanced
teleconferencing technologies. In exchange for this investment, LIVEware has
issued 300,000 shares of common stock, no par value and warrants to purchase
600,000 shares of common stock at $.01 per share. The warrants will cancel upon
LIVEware achieving certain levels of revenues and pretax profit beginning in
fiscal year 2000. If the warrants do not cancel, the Trust may own up to 900,000
shares of LIVEware, which would represent approximately 17.1% of of LIVEware.
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATIONS:
 
RESULTS OF OPERATIONS:
 
<TABLE>
<CAPTION>
                                               THREE MONTHS ENDED    THREE MONTHS ENDED
                                                 MARCH 31, 1998        MARCH 31, 1997
                                               ------------------    ------------------
<S>                                            <C>                   <C>
Description:
  Interest income..........................         $143,147              $104,693
  Management fees..........................           45,780                41,473
  Legal expense............................            4,328                14,840
</TABLE>
 
     INTEREST INCOME: Below is a summary of interest income earned by the Trust
for three months ended March 31, 1998 and 1997.
 
<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED
                                                       --------------------------------
                                                       MARCH 31, 1998    MARCH 31, 1997
                                                       --------------    --------------
<S>                                                    <C>               <C>
Money Market.......................................       $ 55,647          $ 63,423
VisionComm.........................................         17,500            41,270
Kinseth............................................         70,000               -0-
                                                          --------          --------
Total Interest Income..............................       $143,147          $104,693
                                                          ========          ========
</TABLE>
 
     MANAGEMENT FEES: The Trust accrues an annual management fee equal to 2.5%
of the total assets of the Trust paid quarterly.
 
                                        8
<PAGE>   9
                        BERTHEL GROWTH & INCOME TRUST I
            NOTES TO FINANCIAL STATEMENTS (UNAUDITED) -- (CONTINUED)
 
     LEGAL: Legal expenses incurred are associated with the structuring and
monitoring of Trust activities and investments. Additional legal charges were
incurred in 1997 in connection with the formation of the Berthel SBIC as
discussed below.
 
     FORMATION OF SBIC: Berthel SBIC, LLC (the "SBIC"), an entity wholly-owned
by the Trust within the meaning of Section 2(a)(43) of the Investment Company
Act of 1940, has received, from the Small Business Administration (the "SBA"), a
license to operate as a Small Business Investment Company. The Trust has funded
the SBIC with a capital contribution of $5,000,000, the minimum amount eligible
to be contributed in order to receive leverage under the SBA Small Business
Investment Company program. The Trust Advisor and Independent Trustees have the
same responsibilities in the management of the SBIC as they do for the Trust.
The SBIC will attempt to obtain SBA pre-approval for all investments. There is
no guarantee that investments will be approved by the SBA. If an investment has
been completed prior to SBIC approval and is subsequently not approved by the
SBA, the Trust will be required to provide additional funds to the SBIC to
maintain $5,000,000 of "contributed capital" in order to remain eligible to
receive SBA leverage. There is no assurance that the Trust will have the
additional funds needed if the SBA does not approve investments.
 
OTHER POTENTIAL PORTFOLIO COMPANIES AND TRUST ACTIVITIES:
 
     The Trust is working closely with several companies with the intention of
completing investments with them in the very near future. There can be no
assurance that these deals may be completed.
 
LIQUIDITY AND CAPITAL RESOURCES
 
<TABLE>
<CAPTION>
                                                             THREE MONTHS ENDED    THREE MONTHS ENDED
                                                               MARCH 31, 1998        MARCH 31, 1997
                                                             ------------------    ------------------
<S>                                                          <C>                   <C>
MAJOR CASH SOURCE:
  Proceeds from issuance of beneficial shares............         $    -0-              $294,000
  Repayment of note receivable...........................              -0-               275,304
  Liquidation of money market securities.................           93,851                   -0-
MAJOR CASH USE:
  Payments for syndication costs.........................         $    -0-              $ 42,492
  Investment in money market securities..................              -0-               609,409
  Distribution payments to Shareholders..................          144,736                   -0-
</TABLE>
 
     Pending investment in portfolio companies, the Trust has invested
$4,493,747 in bank money accounts at March 31, 1998.
 
     Distributions payable of $881,883 have been accrued as of March 31, 1998.
The Trust will continue to accrue distributions based on 8% simple annual
interest computed on a daily basis until the cumulative distributions to each
investor from the Trust equals 100% of their original investment plus the
priority and underwriting return.
 
     The Trust Advisor is not aware of any regulatory issues that may have a
substantial negative impact on the portfolio companies and is currently
researching for possible investment of Trust funds.
 
     The effect of interest rate fluctuations and inflation on the current Trust
investments is negligible.
 
                                        9
<PAGE>   10
 
                                   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 thereunto duly authorized.
 
                                      BERTHEL GROWTH & INCOME TRUST I
                                      (Registrant)
 
Date 5-11-98                             /s/ RONALD O. BRENDENGEN
                                 -----------------------------------------
                                   Ronald O. Brendengen, Chief Financial 
                                            Officer, Treasurer
 
Date 5-11-98                               /s/ DANIEL P. WEGMANN
                                 -----------------------------------------
                                       Daniel P. Wegmann, Controller
 
                                       10