Exhibit 3.2

GLADSTONE CAPITAL CORPORATION

ARTICLES SUPPLEMENTARY

ESTABLISHING AND FIXING THE RIGHTS AND PREFERENCES

OF TERM PREFERRED SHARES, 6.00% SERIES 2024

Gladstone Capital Corporation, a Maryland corporation (the “Corporation”), hereby certifies to the State Department of Assessments and Taxation of Maryland (the “Department”) that:

FIRST: Under a power contained in Article FOURTH of the charter of the Corporation (the “Charter”), the Board of Directors of the Corporation (the “Board of Directors”), by duly adopted resolutions, reclassified and designated 20,118 authorized but unissued Term Preferred Shares, 6.75% Series 2021, of the Corporation, and also classified and designated 2,979,882 authorized but unissued Term Preferred Shares of the Corporation without designation as to series, each with a par value of $0.001 per share (collectively, the “Shares”), as Term Preferred Shares, 6.00% Series 2024, of the Corporation (the “Series 2024 TP Shares”).

SECOND: Except for such modifications or additions as provided in the following paragraph, a description of the preferences, rights, voting powers, restrictions, limitations as to dividends and other distributions, qualifications and terms and conditions of redemption of the Series 2024 TP Shares is contained under the headings “Definitions” and “Terms Applicable to All Series of Term Preferred Shares” in the Articles Supplementary filed with, and accepted for record by, the Department on October 31, 2011, as corrected by the Certificate of Correction filed with, and accepted for record by, the Department on October 29, 2015 (the “TP Articles Supplementary”).

THIRD: In lieu of or in addition to the preferences, rights, voting powers, restrictions, limitations as to dividends and other distributions, qualifications and terms and conditions of redemption contained under the headings “Definitions” and “Terms Applicable to All Series of Term Preferred Shares” in the TP Articles Supplementary, the Series 2024 TP Shares shall have the preferences, rights, voting powers, restrictions, limitations as to dividends and other distributions, qualifications and terms and conditions of redemption set forth on Exhibit A hereto, which Exhibit A shall constitute an Appendix (as such term is defined in the TP Articles Supplementary).

FOURTH: The Shares have been reclassified and designated, or classified and designated, by the Board of Directors under the authority contained in the Charter.

FIFTH: These Articles Supplementary have been approved by the Board of Directors in the manner and by the vote required by law.

SIXTH: The undersigned acknowledges these Articles Supplementary to be the corporate act of the Corporation and, as to all matters or facts required to be verified under oath, the undersigned acknowledges that, to the best of his knowledge, information and belief, these matters and facts are true in all material respects and that this statement is made under the penalties for perjury.

IN WITNESS WHEREOF, the Corporation has caused these Articles Supplementary to be signed in its name and on its behalf by its Chairman of the Board and Chief Executive Officer and attested to by its Secretary on September 20, 2017.

EXHIBIT A

GLADSTONE CAPITAL CORPORATION

TERM PREFERRED SHARES, 6.00% SERIES 2024

Capitalized terms used herein but not defined herein have the respective meanings therefor set forth in the TP Articles Supplementary.

SECTION 1. Designation as to Series.

Term Preferred Shares, 6.00% Series 2024: A series of 3,000,000 shares of Capital Stock classified as Term Preferred Shares is hereby designated as the “Term Preferred Shares, 6.00% Series 2024” (the ‘‘Series 2024 TP Shares”). Each share of such Series shall have such preferences, rights, voting powers, restrictions, limitations as to dividends and other distributions, qualifications and terms and conditions of redemption, in addition to those required by applicable law and those that are expressly set forth in the Articles and the TP Articles Supplementary (except as the TP Articles Supplementary may be expressly modified by this Appendix), as are set forth in this Exhibit A . The Series 2024 TP Shares shall constitute a separate series of Capital Stock and of the Term Preferred Shares and each Series 2024 TP Share shall be identical. The following terms and conditions shall apply solely to the Series 2024 TP Shares:

SECTION 2. Number of Authorized Shares of Series.

The number of authorized shares is 3,000,000.

SECTION 3. Date of Original Issue with respect to Series.

The Date of Original Issue is September 27, 2017.

SECTION 4. Fixed Dividend Rate Applicable to Series.

The Fixed Dividend Rate is 6.00%.

SECTION 5. Liquidation Preference Applicable to Series.

The Liquidation Preference is $25.00 per share.

SECTION 6. Term Redemption Date Applicable to Series.

The Term Redemption Date is September 30, 2024.

SECTION 7. Dividend Payment Dates Applicable to Series.

The Dividend Payment Dates are the last Business Day of the month of the Dividend Period.

SECTION 8. Non-Call Period Applicable to Series.

The Non-Call Period is the period beginning on the Date of Original of Issue and ending at the close of business on September 30, 2019.

SECTION 9. Modifications to Certain Definitions Applicable to the Series.

The following definitions contained under the heading “Definitions” in the TP Articles Supplementary are hereby modified with respect to the Series 2024 TP Shares as follows:

“Redemption Price” shall mean the Term Redemption Price, the Mandatory Redemption Price, the Optional Redemption Price or the Change of Control Redemption Price.

The following definition contained in the last line of Section 2.2(g)(i) in the TP Articles Supplementary is hereby modified with respect to the Series 2024 TP Shares as follows:

The “Default Rate” on a Series of Term Preferred Shares for any calendar day shall be equal to the Fixed Dividend Rate for such Series plus four percent (4%) per annum.

SECTION 10. Additional Definitions Applicable to the Series.

The following terms shall have the following meanings (with terms defined in the singular having comparable meanings when used in the plural and vice versa), unless the context otherwise requires:

“Change of Control Triggering Event” means the occurrence of any of the following: (1) the direct or indirect sale, lease, transfer, conveyance or other disposition (other than by way of merger or consolidation), in one or more series of related transactions, of all or substantially all of the Corporation’s assets and the assets of the Corporation’s subsidiaries, taken as a whole, to any Person, other than the Corporation or one of its subsidiaries; (2) the consummation of any transaction (including, without limitation, any merger or consolidation) the result of which is that any Person becomes the beneficial owner (as defined in Rules 13d-3 and 13d-5 under the Exchange Act), directly or indirectly, of more than 50% of the Corporation’s outstanding Voting Stock or other Voting Stock into which the Corporation’s Voting Stock is reclassified, consolidated, exchanged or changed, measured by voting power rather than number of shares; (3) the Corporation consolidates with, or merges with or into, any Person, or any Person consolidates with, or merges with or into, the Corporation, in any such event pursuant to a transaction in which any of the Corporation’s outstanding Voting Stock or the Voting Stock of such other Person is converted into or exchanged for cash, securities or other property, other than any such transaction where the shares of the Corporation’s Voting Stock outstanding immediately prior to such transaction constitute, or are converted into or exchanged for, a majority of the Voting Stock of the surviving Person or any direct or indirect parent company of the surviving Person immediately after giving effect to such transaction; or (4) the adoption of a plan relating to the Corporation’s liquidation or dissolution. Notwithstanding the foregoing, a transaction will not be deemed to involve a Change of Control Triggering Event under clause (2) above if (i) the Corporation becomes a direct or indirect wholly-owned subsidiary of a holding company and (ii)(A) the direct or indirect holders of the Voting Stock of such holding company immediately following that transaction are substantially the same as the holders of the Corporation’s Voting Stock immediately prior to that transaction or (B) immediately following that transaction no Person (other than a holding company satisfying the requirements of this sentence) is the beneficial owner, directly or indirectly, of more than 50% of the Voting Stock of such holding company.

“Dividend Period” means, with respect to each Series 2024 TP Share, in the case of the first Dividend Period, the period beginning on the Date of Original Issue for such Series and ending on and including October 31, 2017 and for each subsequent Dividend Period, the period beginning on and including the first calendar day of the month following the month in which the previous Dividend Period ended and ending on and including the last calendar day of such month.

“Voting Stock” means, with respect to any specified Person that is a corporation as of any date, the capital stock of such Person that is at the time entitled to vote generally in the election of the directors of such Person.

SECTION 11. Modifications to Terms of Term Preferred Shares Applicable to the Series.

The following provisions contained under the heading “Terms Applicable to All Series of Term Preferred Shares” in the TP Articles Supplementary are hereby modified with respect to the Series 2024 TP Shares as follows:

(a) Notwithstanding the requirement in Section 2.5(a), (b) or (c) of the TP Articles Supplementary or in Section 12(a)(i) below that the Redemption Price per Term Preferred Share includes an amount equal to all unpaid dividends and distributions on such share accumulated to (but excluding) the Redemption Date, if such Redemption Date occurs after the applicable record date for a dividend but on or prior to the related Dividend Payment Date, the

dividend payable on such Dividend Payment Date in respect of such Term Preferred Shares shall be payable on such Dividend Payment Date to the holders of record of such Term Preferred Shares at the close of business on the applicable record date, and shall not be payable as part of the Redemption Price for such Term Preferred Shares.

(b) Notwithstanding the first sentence of Section 2.5(b)(ii) of the TP Articles Supplementary, in the event that shares of Preferred Stock are redeemed pursuant to Section 2.5(b) of the TP Articles Supplementary, the Corporation may at its sole option, but is not required to, redeem a sufficient number of shares of any Series of Term Preferred Shares pursuant to Section 2.5(b) that, when aggregated with other shares of Preferred Stock redeemed by the Corporation, would result, if deemed to have occurred immediately prior to the opening of business on the Asset Coverage Cure Date, in the Corporation having Asset Coverage on such Asset Coverage Cure Date of up to and including 240%.

(c) Notwithstanding anything to the contrary in the TP Articles Supplementary, if the Redemption Date is the Term Redemption Date, the deposit of Deposit Securities shall be made no later than 15 calendar days prior to the Term Redemption Date.

SECTION 12. Additional Terms and Provisions Applicable to the Series.

The following provisions shall also apply to the Series 2024 TP Shares:

(a) Mandatory Redemption upon Change of Control.

(i) If a Change of Control Triggering Event occurs with respect to the Series 2024 TP Shares, unless the Corporation has exercised its option to redeem such Series 2024 TP Shares pursuant to Section 2.5(c) of the TP Articles Supplementary, the Corporation shall redeem all of the outstanding Series 2024 TP Shares (the “Change of Control Redemption”) at a price per share equal to the Liquidation Preference per Series 2024 TP Share, plus an amount equal to all unpaid dividends on such Series 2024 TP Share accumulated to (but excluding) the Redemption Date (whether or not earned or declared by the Corporation, but excluding interest thereon) (the “Change of Control Redemption Price”).

(ii) If the Corporation shall be required to redeem all of the outstanding Series 2024 TP Shares pursuant to paragraph (i) above, the Corporation shall deliver a Notice of Redemption, by overnight delivery, by first class mail, postage prepaid or by Electronic Means to Holders thereof, or request the Redemption and Paying Agent, on behalf of the Corporation, to promptly do so by overnight delivery, by first class mail, postage prepaid or by Electronic Means. Such Notice of Redemption shall be provided not more than forty-five (45) calendar days prior to the Redemption Date; provided, however, that such Notice of Redemption will, if mailed prior to the date of consummation of the Change of Control Triggering Event, state that the Change of Control Redemption is conditioned on the Change of Control Triggering Event occurring and, provided further, that if, by the date that is three Business Days prior to the date fixed for redemption in such Notice of Redemption, the Change of Control Triggering Event shall not have occurred, the Redemption Date shall be extended until a date that is no more than three Business Days after the date on which the Change of Control Triggering Event occurs.

(iii) Upon the date of the deposit of Deposit Securities for the Change of Control Redemption, all rights of the Holders of the Series 2024 TP Shares so called for redemption shall cease and terminate except the right of the Holders thereof to receive the Change of Control Redemption Price and such Series 2024 TP Shares shall no longer be deemed Outstanding for any purpose whatsoever (other than (A) the transfer thereof prior to the applicable Redemption Date and (B) the accumulation of dividends thereon in accordance with the terms thereof up to (but excluding) the applicable Redemption Date, which accumulated dividends, unless previously or contemporaneously declared and paid as contemplated by the last sentence of Section 2.5(d)(vi) of the TP Articles Supplementary, shall be payable only as part of the Change of Control Redemption Price on the Redemption Date). The Corporation shall be entitled to receive, promptly after the Redemption Date, any Deposit Securities in excess of the aggregate Change of Control Redemption Price of the Series 2024 TP Shares called for redemption on the Redemption Date. Any Deposit Securities so deposited that are unclaimed at the end of ninety (90) calendar days from the Redemption Date shall, to the extent permitted by law, be repaid to the Corporation, after which the Holders of the Series 2024 TP Shares so called for redemption shall look only to the Corporation for payment of the Change of Control Redemption Price. The Corporation shall be entitled to receive, from time to time after the Redemption Date, any interest on the Deposit Securities so deposited.

(b) Information Rights. During any period in which the Corporation is not subject to the reporting requirements of Section 13 or 15(d) of the Exchange Act and any Series 2024 TP Shares are outstanding, the Corporation shall provide holders of Series 2024 TP Shares, without cost, copies of the SEC Reports that the Corporation would have been required to file with the Securities and Exchange Commission pursuant to Section 13 or 15(d) of the Exchange Act if the Corporation were subject to such provisions.