UNITED STATES SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

SCHEDULE 14A

(Rule 14a-101)

INFORMATION REQUIRED IN PROXY STATEMENT

SCHEDULE 14A INFORMATION

Proxy Statement Pursuant to Section 14(a) of the Securities

Exchange Act of 1934

Filed by the Registrant þ

Filed by a Party other than the Registrant ¨

Check the appropriate box:

Gladstone Capital Corporation

(Name of Registrant as Specified in its Charter)

Not Applicable

(Name of Person(s) Filing Proxy Statement if Other Than the Registrant)

Payment of Filing Fee (Check the appropriate box):

þ No fee required.

¨ Fee computed on table below per Exchange Act Rules 14a-6(i)(1) and 0-11.

On Wednesday, January 7, 2015, at 9:00 a.m. Eastern Standard Time, Gladstone Capital Corporation (the “Company”) held a conference call regarding the proposals included in the Company’s Definitive Proxy Statement (the “Proxy”), which was filed with the U.S. Securities and Exchange Commission on December 12, 2014.

A script of the call follows:

Hello and good morning. This is David Gladstone, Chairman.

This is a special call to explain the items in the proxy for shareholders and analysts of Gladstone Capital Corporation, common stock NASDAQ trading symbol GLAD and preferred stock NASDAQ trading symbol GLADO.

Thank you all for calling in. We are happy to talk to shareholders and you always have an open invitation to visit us here in the Washington, DC area. Please stop by our office in McLean, Virginia and say hello. You will see some of the finest people in the business.

We also invite you all to come to the shareholders meeting on February 12, 2015 at 11am Eastern Time at the Hilton McLean Tysons Corner, located at 7920 Jones Branch Drive, in McLean, Virginia.

If you are not coming to the meeting, then please vote your shares using your proxy so that we get the votes in.

There are 4 ways you can vote before the meeting:

Regulations only allow your broker to vote your shares for you on routine matters – incidentally, none of the matters to be voted upon at this meeting are routine. Thus, your broker may not vote any of your shares for you. As a result, the cost to your company to round up the votes by calling and asking shareholders to vote their shares to ensure a quorum is now a major expense. And that takes away dollars that could otherwise be paid in distributions to shareholders.

Before I begin to review the matters up for vote at this year’s annual meeting, I need to read a statement about forward looking statements.

This conference call may include statements that may constitute “forward-looking statements” within the meaning of Securities Act of 1933 and of the Securities Exchange Act of 1934 including statements with regard to the future performance of the Company.

These forward-looking statements inherently involve certain risks and uncertainties, even though they are based on our current plans, which we believe to be reasonable.

There are many factors that may cause our actual results to be materially different from any future results that are expressed or implied by these forward-looking statements, including those factors listed under the caption “Risk Factors” in all our Form 10K fillings as filed with the Securities and Exchange Commission that can be found on our web site at www.GladstoneCapital.com and the SEC’s web site (www.SEC.gov).

The Company undertakes no obligation to publicly update or revise any forward-looking statements, whether as a result of new information, future events or otherwise, except as required by law.

Again, thank you for calling in.

Before starting with the matters in this year’s Proxy, I want you to know that we will have our quarterly earnings call for the quarter ended December 31, 2014, at the end of January, so I will not be able to answer on this call, questions about the 10-Q we are planning to file for the December quarter end. Look for that press release or go to our web site and sign up for email notification of events at your company so you get the information when it is posted. You can also follow us on Twitter, user name ‘GladstoneComps’ or on Facebook, keyword ‘The Gladstone Companies.’

I can report to you that our fund is performing well. In fiscal year 2014, our team accomplished the following:

As noted in our recent press releases, we closed a number of attractive new investments during the December 31, 2014 quarter which we believe represents a very positive start to fiscal year 2015. We will comment more on these in our first 2015 fiscal quarter end Form 10Q we expect to file at the end of this month, so please do not ask any questions about the earnings for the December quarter because until we release our quarterly numbers I cannot discuss them at all.

Our quarterly board meeting is scheduled for next week and I expect our board to declare our monthly distributions as we have before.

Now let’s turn to the Proxy. In the Proxy we have asked shareholders to vote on two things.

1. First, we are asking you to elect three directors. Two of the directors on the ballot will represent preferred shareholders and will be elected solely by the preferred shareholders. The election of directors is something that we do every year.

2. Second, we are asking shareholders to approve a proposal to authorize our fund to sell shares of our common stock at a price below the then current net asset value per share. Many Business Development Companies, or BDCs, ask their shareholders to do this because many BDCs stock prices are below net asset value per share.

As you all know, as a Regulated Investment Company under the IRS rules, our fund must pay out 98% of our income to avoid paying taxes. And we do that each year.

This means the only way to grow is to raise equity or debt. As a BDC, we are limited by the SEC rules to having less than our equity in the amount of debt (in other words, a 1:1 debt to equity ratio) so none of the companies like ours are highly leveraged, and our balance sheet is typically lower leveraged than that of our peers. And that is a good thing.

To grow the assets and earnings of our fund we will need to raise equity in the future.

We need your vote to put in place the ability to sell shares at below net asset value. In the current environment, with the stock trading at or below net asset value, without your vote, we could not raise equity except by doing a rights offering. Rights offerings are very expensive to existing shareholders because the short sellers come in and knock down the price of the stock. We had that happen to us in 2008. So we do not want to do that except as an emergency.

Doing overnight offerings or an offering under an “at-the-market” program, as some other BDCs are currently doing, would work well to raise equity and would not let the short sellers come in and push down the stock price. It may be advantageous to raise some equity in a manner that would not cause meaningful dilution of our existing shareholders and would permit the fund to grow and hopefully increase the dividend. But to do either of these types of offerings, we need your approval to sell at below net asset value. Net asset value per share at September 30, 2014, was $9.51, while the current stock price yesterday was $8.50.

We need this proposal to pass so we have an alternative to a rights offering. And the government requires us to get this item passed by shareholders every year and that too runs up the cost of running this fund because of the cost of getting this Proxy out and gathering votes. So we ask you to please review the Proxy and vote for this one.

Now I must ask all of you to please vote your shares. It is ever so costly and time consuming to get shareholders to vote. The fund spends thousands of dollars trying to contact voters to vote on these issues, so please vote your shares. I would like to pay that money out as a dividend and not spend it on efforts like this.

Our common dividend, by the way, has been $0.07 per month, a run rate of $0.84 per year. The Board will meet next week to vote on declaring the dividend for January, February and March 2015.

In looking at the economy in general, indicators seem to be moving in the right direction, albeit slowly. The U.S. recovery has been prolonged and many businesses, including some in our portfolio, are still feeling the lingering impacts of the recent recession. Our priorities for 2015 will be to manage the more challenging credits in the portfolio and build on the new origination momentum which we have begun to see in the first quarter of our fiscal 2015. We will continue to focus on building our portfolio with investments in strong operating cash flow businesses in stable to growing industries.

Despite some of the broader investing market pressures our fund like other middle market loan funds are feeling, we continue to be optimistic that we are well positioned to originate lower leverage and attractively priced investments and can generate solid asset and income growth over the coming quarters, which should be accretive to our shareholders in the future. Our new President and his team are dedicated to reinforcing our position as one of the leading debt providers servicing small and medium-sized, privately-held companies in the U.S. while producing consistent returns for our shareholders.

We invite you all to come to the shareholders meeting on February 12, 2015 at 11:00 a.m. Eastern Time at the Hilton McLean Tysons Corner, located at 7920 Jones Branch Drive in McLean, Virginia. We would like to see you all and talk about the Company at that meeting. If you are not coming, or even if you are, please vote your shares of stock so that we can move forward with our investing strategies and grow the business. Remember that you can vote any of the 4 ways we discussed earlier: by mailing in your proxy, by calling your broker, by calling 1-800-690-6903, but you have to have your proxy card with the proxy control number to vote by phone, or by going to www.proxyvote.com, again with your proxy card and proxy control number.

If you haven’t received your proxy in the mail yet, you should call your broker and get them to send you a replacement. But please vote so we can continue to grow the Company.