Underwriters are exercising an option to purchase an additional 2.25 million shares in Wesco Aircraft Holdings Inc. in a secondary offering from the company’s largest shareholder, the Carlyle Group.

Carlyle, a Washington, D.C. private equity firm, had already agreed to sell 15 million shares at $16 a share in the Valencia aerospace parts supplier. The additional 2.25 million shares are also being purchased for $16. When the sale closes on May 29, Carlyle will have 38.6 percent stake in Wesco.

Carlyle bought a majority stake in the company in 2006 when it was privately held, and took it public in July 2011, raising $315 million in the initial public offering. The proceeds of the secondary offering are going to Wesco CEO Randy J. Snyder and Carlyle.

Wesco Aircraft is one of the world’s largest distributors of aerospace parts. It has more than 1,200 employees in 12 countries.

Barclays Capital Inc., J.P. Morgan Securities LLC, Citigroup Global Markets Inc., Morgan Stanley & Co. LLC and William Blair & Company, L.L.C. are acting as joint book-running managers and Barclays Capital Inc. and J.P. Morgan Securities LLC are serving as representatives of the several underwriters for the offering.