The company is selling shares at $42 to $45 each, according to a filing today with the Securities and Exchange Commission. The shares had been offered for $32 to $35 apiece. At the new top end of the range, LinkedIn would raise $405.7 million, about 29 percent more than previously sought.

LinkedIn is still selling 7.84 million shares, with a so- called overallotment option to offer another 1.18 million shares. The company will have 94.5 million shares outstanding after the offering, giving the company a valuation between $3.97 billion and $4.25 billion at the current share offerings.

The Mountain View, California-based company is one of several high-profile U.S. Internet companies planning to go public. Online coupon provider Groupon Inc. is discussing an IPO that would value it at about $25 billion, people familiar with the matter said this year. Facebook Inc. has been meeting with bankers since April to discuss a possible IPO, CNBC reported yesterday, and was valued at $65 billion, the research firm Nyppex LLC said last month.

LinkedIn said it plans to use the proceeds of its IPO to fund existing operations and to expand the business, which may include buying other companies or technologies. In addition to some of LinkedIn’s management, investors selling shares include Boston-based private-equity firm Bain Capital LLC and New York- based Goldman Sachs Group Inc.