LIMITED POWER OF ATTORNEY FOR

                        SECTION 16 REPORTING OBLIGATIONS

    Know all by these presents, that the undersigned's hereby makes, constitutes
and appoints Jeffrey F. Brotman and Mark Rosenstein as the undersigned's true
and lawful attorney-in-fact, with full power and authority as hereinafter
described on behalf of and in the name, place and stead of the undersigned to:

(1) prepare, execute, acknowledge, deliver and file Forms 3, 4, and 5 (including
any amendments thereto) with respect to the securities of Osprey Technology
Acquisition Corp. (the "Company"), with the United States Securities and
Exchange Commission, any national securities exchanges and the Company, as
considered necessary or advisable under Section 16(a) of the Securities Exchange
Act of 1934 and the rules and regulations promulgated thereunder, as amended
from time to time (the "Exchange Act");

(2) seek or obtain, as the undersigned's representative and on the undersigned's
behalf, information on transactions in the Company's securities from any third
party, including brokers, employee benefit plan administrators and trustees, and
the undersigned hereby authorizes any such person to release any such
information to the undersigned and approves and ratifies any such release of
information; and

(3) perform any and all other acts which in the discretion of such attorney-in-
fact are necessary or desirable for and on behalf of the undersigned in
connection with the foregoing.

The undersigned acknowledges that:

(1) this Power of Attorney authorizes, but does not require, such attorney-in-
fact to act in their discretion on information provided to such attorney-in-fact
without independent verification of such information;

(2) any documents prepared and/or executed by such attorney-in-fact on behalf of
the undersigned pursuant to this Power of Attorney will be in such form and will
contain such information and disclosure as such attorney-in-fact, in his or her
discretion, deems necessary or desirable;

(3) neither the Company nor such attorney-in-fact assumes (i) any liability for
the undersigned's responsibility to comply with the requirement of the Exchange
Act, (ii) any liability of the undersigned for any failure to comply with such
requirements, or (iii) any obligation or liability of the undersigned for profit
disgorgement under Section 16(b) of the Exchange Act; and

(4) this Power of Attorney does not relieve the undersigned from responsibility
for compliance with the undersigned's obligations under the Exchange Act,
including without limitation the reporting requirements under Section 16 of the
Exchange Act.

    The undersigned hereby gives and grants the foregoing attorney-in-fact full
power and authority to do and perform all and every act and thing whatsoever
requisite, necessary or appropriate to be done in and about the foregoing
matters as fully to all intents and purposes as the undersigned might or could
do if present, hereby ratifying all that such attorney-in-fact of, for and on
behalf of the undersigned, shall lawfully do or cause to be done by virtue of
this Limited Power of Attorney.

    This Power of Attorney shall remain in full force and effect until revoked
by the undersigned in a signed writing delivered to such attorney-in-fact.

    IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 30th day of October, 2019.

                                      By:  /s/ Robert B. Henske
                                           ---------------------
                                      Name: Robert B. Henske