POWER OF ATTORNEY

      Know all by these presents, that the undersigned hereby constitutes and
appoints Adam M. Kleinman, signing singly, the undersigned's true and lawful
attorney-in-fact to:

           (1)    execute for and on behalf of the undersigned, in the
      undersigned's capacity as a deemed officer, director, 10% owner and/or
      "other" of Great Elm Capital Corp. (the "Company"), Forms 3, 4 and 5 in
      accordance with Section 16(a) of the Securities Exchange Act of 1934, as
      amended (the "Exchange Act"), and the rules thereunder;

           (2)    do and perform any and all acts for and on behalf of the
      undersigned which may be necessary or desirable to complete and execute
      any such Form 3, 4 or 5, complete and execute any amendment or amendments
      thereto, and timely file such form with the United States Securities and
      Exchange Commission and any stock exchange or similar authority; and

           (3)    take any other action of any type whatsoever in connection
      with the foregoing which, in the opinion of such attorney-in-fact, may be
      of benefit to, in the best interest of, or legally required by, the
      undersigned, it being understood that the documents executed by such
      attorney-in-fact on behalf of the undersigned pursuant to this Power of
      Attorney shall be in such form and shall contain such terms and conditions
      as such attorney-in-fact may approve in such attorney-in-fact's
      discretion.

      The undersigned hereby grants to such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be
done by virtue of this Power of Attorney and the rights and powers herein
granted.  The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, is not assuming, nor
is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Exchange Act.

      The execution by the undersigned of this Power of Attorney hereby
expressly revokes and terminates any powers of attorney previously granted by
the undersigned relating to Forms 3, 4 and 5 with respect to the undersigned's
holdings of and transactions in securities issued by the Company.  This Power of
Attorney shall remain in full force and effect until the undersigned is no
longer required to file Forms 3, 4 and 5 with respect to the undersigned's
holdings of and transactions in securities issued by the Company, unless earlier
revoked by the undersigned in a signed writing delivered to the foregoing
attorneys-in-fact.

      IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of March 18, 2019.

                                          /s/ Keri Davis
                                          --------------------------------------
                                          Keri Davis