By Alexei Oreskovic

SAN FRANCISCO (Reuters) - Facebook Inc's advertising business grew at its fastest clip since before the company's May initial public offering, helping the company's revenue expand 40 percent to $1.585 billion.

Shares of Facebook were down 5.9 percent to $29.40 in after hours trading on Wednesday.

Facebook, the world's largest online social networking service, said net income in the fourth quarter was $64 million, or 3 cents a share, compared to $302 million, or 14 cents a share in the year-ago period.

Excluding certain items, Facebook said it earned 17 cents a share.

Facebook has ramped up its online advertising services in recent months, putting a greater emphasis on mobile ads and introducing capabilities that let marketers target Facebook users based on their Web browsing history.

Advertising revenue in the fourth quarter grew 41 percent to $1.33 billion, with mobile ads representing 23 percent of Facebook's ad revenue.

Facebook's overall fourth-quarter revenue was $1.585 billion, versus $1.131 billion in the year-ago period.

(Reporting by Alexei Oreskovic; Editing by Phil Berlowitz)