GAMCO GLOBAL SERIES FUNDS, INC.

Supplement dated December 27, 2019

to

The Gabelli Global Rising Income and Dividend Fund’s Summary Prospectus dated April 30, 2019

This supplement amends certain information in the Summary Prospectus (the “Summary Prospectus”), dated April 30, 2019, of The Gabelli Global Rising Income and Dividend Fund (the “Fund”), a series of GAMCO Global Series Funds, Inc. Unless otherwise indicated, all other information included in the Summary Prospectus, or any previous supplements thereto, that is not inconsistent with the information set forth in this supplement remains unchanged. Capitalized terms not otherwise defined in this supplement have the same meaning as in the Summary Prospectus.

Closing of Class AAA, Class A and Class C Shares

The Board of Directors (the “Board”) of GAMCO Global Series Funds, Inc., on behalf of the Fund, has approved the closing of the Fund’s Class AAA, Class A and Class C Shares to new investors.

Effective January 27, 2020, (the “Effective Date”) the Fund’s Class AAA, Class A and Class C Shares will be “closed to purchases from new investors.” “Closed to purchases from new investors” means: (i) with respect to Class AAA and Class A Shares, no new investors may purchase shares of such classes, but existing shareholders may continue to purchase additional shares of such classes after the Effective Date, and (ii) with respect to Class C Shares, neither new investors nor existing shareholders may purchase any additional shares of such class after the Effective Date. These changes will have no effect on existing shareholders’ ability to redeem shares of the Fund as described in the Fund’s Summary Prospectus.

Additionally, on the Effective Date Class I shares of the Fund are available to investors with a minimum initial investment amount of $1,000 and purchasing shares directly through the Distributor, or investors purchasing Class I shares through brokers or financial intermediaries that have entered into selling agreements with the Distributor specifically with respect to Class I shares.

Since the minimum initial investment amount for the Fund’s Class I shares purchased directly through the Distributor is the same as that for all other classes of the Fund’s shares, shareholders still eligible to purchase Class AAA and Class A shares of the Fund on or after the Effective Date should instead consider purchasing Class I shares since Class I shares carry no sales load and no ongoing distribution fees. Investors and shareholders who wish to purchase shares of the Fund through a broker or financial intermediary should consult their broker or financial intermediary with respect to the purchase of shares of the Fund.

Please refer to the Fund’s statutory prospectus for additional information about share class conversions and exchanges among funds managed by the Adviser or its affiliates.

STOCKHOLDERS SHOULD RETAIN THIS SUPPLEMENT FOR FUTURE REFERENCE