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Filed Pursuant to Rule 497(e)

Registration No. 33-66262

GAMCO GLOBAL SERIES FUNDS, INC.

The Gabelli International Small Cap Fund

Supplement dated February 8, 2021, to The Gabelli International Small Cap Fund’s Summary Prospectus and GAMCO Global Series Funds’ Statutory Prospectus, each dated April 29, 2020.

Effective February 1, 2021, Mr. Gustavo Pifano and Mr. Ashish Sinha have been added to the portfolio management team for The Gabelli International Small Cap Fund (the “Fund”).

To reflect the changes, please note the following:

The following is added to the end of the sub-section “Management – The Portfolio Manager” in the Summary Prospectus and after the first paragraph of the section “Management of The Funds – The Portfolio Managers” of the Statutory Prospectus:

In managing the portfolio of The Gabelli International Small Cap Fund, the Adviser also uses the services of Gustavo Pifano and Ashish Sinha, investment professionals of an affiliate, GAMCO Asset Management (UK) Limited (“GAMCO UK”). Mr. Pifano joined the firm in 2008 and is an Assistant Vice President for research based in London. He covers the industrial and consumer sectors with a focus on small-cap stocks. Mr. Pifano holds a Bachelor of Business Administration in Finance from the University of Miami and an MBA from the University of Oxford Said Business School.

Mr. Sinha joined GAMCO UK in 2012 as a research analyst and is an Assistant Vice President. Mr. Sinha holds a Bachelor of Business Administration from IMS, India and a Master of International Business from the Indian Institute of Foreign Trade, India. He is a Chartered Financial Analyst.

In keeping with applicable regulatory guidance, GAMCO UK entered into a Memorandum of Understanding (“MOU”) with the Adviser pursuant to which GAMCO UK is considered a “Participating Affiliate” of the Adviser as that term is used in relief granted by the staff of the Securities and Exchange Commission allowing U.S. registered investment advisers to use portfolio management and trading resources of advisory affiliates subject to the supervision of a registered adviser.

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Filed Pursuant to Rule 497(e)

Registration No. 33-66262

GAMCO GLOBAL SERIES FUNDS, INC.

The Gabelli International Small Cap Fund

Supplement dated February 8, 2021, to the Statement of Additional Information of

The GAMCO Global Series Funds Inc.

dated April 29, 2020.

Effective February 1, 2021, Mr. Gustavo Pifano and Mr. Ashish Sinha have been added to the portfolio management team for the Gabelli International Small Cap Fund (the “Fund”).

To reflect the addition, please note the following:

In the “Investment Advisory and Other Services” section, under the “Other Accounts Managed” sub-section, the following is added with information as of December 31, 2020:

EXCLUDES INTERNATIONAL SMALL CAP FUND:

Under the “Potential Conflicts of Interest” subsection, the following is added:

Compensation Structure for Portfolio Managers other than Mario J. Gabelli

The compensation of the portfolio managers for each of the Global Content & Connectivity Fund, the Global Growth Fund, the International Small Cap Fund, and the Global Mini Mites Fund other than Mr. Gabelli is structured to enable the Adviser to attract and retain highly qualified professionals in a competitive environment. The portfolio managers receive a compensation package that includes a minimum draw or base salary, equity based incentive compensation via awards of stock options, and incentive-based variable compensation based on a percentage of net revenues received by the Adviser for managing a Fund to the extent that the amount exceeds a minimum level of compensation, and discretionary bonuses. Net revenues are determined by deducting from gross investment management fees certain of the Firm’s expenses (other than the respective portfolio manager’s compensation) allocable to the respective Fund. Compensation for managing accounts that have a performance based fee will have two components. One component is based on a percentage of net revenues received by the adviser for managing the account. The second component is based on absolute performance of the account, with respect to which a percentage of the performance fee is paid to the portfolio manager(s). These methods of compensation are based on the premise that superior long term performance in managing a portfolio should be rewarded with higher compensation as a result of growth of assets through appreciation and net investment activity. The level of equity based incentive and incentive-based variable compensation is based on an evaluation by the Adviser’s parent, GBL, of quantitative and qualitative performance evaluation criteria.

Compensation Structure for Mario J. Gabelli

Mr. Gabelli receives incentive-based variable compensation based on a percentage of net revenues received by the Adviser for managing the GRID Fund and the Global Mini Mites Fund. Net revenues are determined by deducting from gross investment management fees the Firm’s expenses (other than Mr. Gabelli’s compensation) allocable to the GRID Fund and the Global Mini Mites Fund. Additionally, he receives similar incentive-based variable compensation for managing other accounts within GBL and its affiliates. This method of compensation is based on the premise that superior long term performance in managing a portfolio should be rewarded with higher compensation as a result of growth of assets through appreciation and net investment activity. The level of compensation is not determined with specific reference to the performance of any account against any specific benchmark. One of the other registered investment companies managed by Mr. Gabelli has a performance (fulcrum) fee arrangement for which his compensation is adjusted up or down based on the performance of the investment company relative to an index. Four closed-end registered investment companies managed by Mr. Gabelli have arrangements whereby the Adviser will only receive its investment advisory fee attributable to the liquidation value of outstanding preferred stock (and Mr. Gabelli would only receive his percentage of such advisory fee) if certain performance levels are met. Mr. Gabelli manages other accounts with performance fees. Compensation for managing these accounts has two components. One component of his compensation is based on a percentage of net revenues received by the Adviser for managing the account. The second component is based on absolute performance of the account, with respect to which a percentage of such performance fee is paid to Mr. Gabelli. As an executive officer of the Adviser’s parent company, GBL, Mr. Gabelli also receives ten percent of the net operating profits of the parent company. Additionally, Mr. Gabelli receives a percentage of net management fees as a relationship manager of accounts managed by affiliates. Mr. Gabelli receives no base salary, no annual bonus, and no stock options. Mr. Gabelli may enter into and has arrangements to defer or waive his compensation.

Under the “Ownership of Shares in the Funds” sub-section, the following is added:

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* Key to Dollar Ranges – Information as of December 31, 2020

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