Bold, brave moves are fast becoming the hallmark of Turkish Airlines, one of the world’s fastest-growing carriers. At a time when many airlines are struggling to stay aloft, Turkish Air is expanding aggressively. It now flies to 98 countries — that’s more than any other airline — and it is quickly ticking off all the boxes needed to become a brand-name global carrier.

Since 2003, when Turkey deregulated its airline industry, Turkish Airlines has nearly quadrupled its passengers, tripled its aircraft, and doubled its number of destination cities. Its fleet is half the average age (6½ years) of its European competitors. Flatbed business seats and “star chefs” have earned it Skytrax’s title of Best European Airline two years in a row. Some analysts have begun to compare Turkish Airlines to Gulf carriers Emirates, Qatar Airways, and Abu Dhabi-based Etihad, which pride themselves on customer service. In 2010 it unveiled a slick global marketing campaign featuring stars such as Kobe Bryant and Barcelona footballer Lionel Messi. The airline’s investments appear to be paying off: In the first nine months of 2012, Turkish Airlines’ profit climbed 665%, to about $482 million, on sales of $6.2 billion.

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The company certainly benefits from a growing domestic economy and a rise in tourism to Turkey: Some 35 million leisure travelers visit the country annually, up from 14 million in 2003. Now CEO Temel Kotil is pushing the airline to capitalize on its advantageous geography (Istanbul is a three- to four-hour flight from many cities in Europe, Asia, and Africa) to turn the airline into a hub carrier for international travel. “We’re Asia and Europe at the same time,” Kotil says.

Last year the airline added routes to 22 cities, including Edinburgh, the Maldives, and, yes, Mogadishu. Dozens more destinations are slated for 2013, including Houston’s George Bush International Airport. In all, Turkish Airlines has increased its network of routes by 43% since 2009.

Kotil is also capitalizing on the woes of European airlines. Hungary’s flagship carrier, Malev, and Spain’s Spanair have gone out of business, while SAS and Air France-KLM, among others, have cut flights.

Turkish Airlines has managed to keep operating costs relatively low with its newer, more fuel-efficient planes and the country’s cheap workforce. Analysts say the airline has been helped along by the government’s support, particularly in terms of infrastructure investment — in January, Turkey opened bidding for a construction contract to build a third airport in Istanbul, which, according to media reports, will be one of the largest in the world.

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But Kotil acknowledges the airline’s steep and speedy ascent is not without risks — like maintaining the same quality training, management, and service across the enterprise. “We’re growing everywhere.” Indeed, Turkish Airlines is widely rumored to be in talks with Lufthansa about a joint venture or other alliance.

Kotil declines to comment on any deals; he says his goal is for Turkish Airlines to fly 2,000 flights a day, double its current levels. (By comparison, United Airlines operates 5,000 flights a day.) And while Turkish Airlines has long ceased to be a government-controlled entity (it was privatized in 2006; the government still owns a 49% stake), Kotil sees its expansion as a point of pride for his country. “Istanbul has been one of the major cities in Europe for centuries,” he says. “In the last century it lost momentum; in the 21st it’s coming back. Turkey is a part of everything.” Including, if Kotil’s bets pay off, the global airline industry.

This story is from the February 25, 2013 issue of Fortune.