SAN FRANCISCO – Peter Thiel, the billionaire venture capitalist who led the first outside investment in Facebook, has created a new firm to back established technology startups.

Mithril Capital Management, based in San Francisco, has raised $402 million to invest in growth-stage companies that are transitioning from small startups into larger businesses, Ajay Royan, managing general partner, said.

Thiel, 44, made his initial fortune as a co-founder of online payments pioneer PayPal Inc. before starting hedge fund Clarium Capital Management. Mithril plans to make smaller investments than Clarium and larger bets than Founders Fund Management, Thiel’s other venture-capital group, Royan said.

“There’s a space in the investment landscape,” said Royan, a former managing director at Clarium. “We are focused on the inflection point when companies have emerged beyond the startup stage and they are ready to achieve scale and dominance in their market.”

Thiel is chairman of Mithril’s investment committee and the firm’s largest individual investor. Mithril also raised money from institutional investors, including Allen & Co. in New York, Royan said.

The size of the fund dwarfs the $16.9 million of Fraser McCombs Ventures, the highest amount raised by a new firm in the first three months of this year, according to the National Venture Capital Association. Venture fundraising totaled $4.88 billion in the first quarter, led by Andreessen Horowitz’s $1.5 billion fund.

Thiel’s fortune has grown with the recent public offerings of Facebook, Zynga and LinkedIn, social-media companies he backed from early stages. His personal wealth totals $2.5 billion, according to the Bloomberg Billionaires Index.

At Clarium, bets on oil prices, currencies and stocks caused the hedge fund to lose 90 percent of its assets from its peak of more than $7 billion in mid-2008 to the end of 2010. Last year, the company said it would shift to invest more in private technology companies.

Thiel also teaches a course at Stanford University and has set aside money for the Thiel Foundation. The non-profit organizes the 20 Under 20 Thiel Fellowship program, which pays students as much as $100,000 each over two years to drop out of college and pursue startups.

Mithril investments will range from less than $20 million to as much as $100 million, and will center on entrepreneurs tackling challenges in areas like biotechnology, energy and artificial intelligence, Royan said.

“These are all spaces where the Silicon Valley approach can make a huge difference,” he said.