Texas Air Corp., the Houston-based airline that made an unsuccessful bid to acquire Trans World Airlines Inc. this summer, yesterday made a $250 million offer to acquire Frontier Holdings Inc., the Denver-based parent of Frontier Airlines.

The tender offer from Texas Air, headed by Frank Lorenzo, of $20 a share for up to 7 million shares of the stock of the financially-troubled company is an attempt to outbid an employe group that offered $17 a share. In addition to the 7 million shares, which represent 51 percent of Frontier's stock, Texas Air plans to acquire the rest of the company's 12.5 million total shares for the same price if it receives Department of Transportation approval for the acquisition.

Despite Texas Air's announcement yesterday, Frontier plans to hold a special shareholder meeting Oct. 30 to vote on the employe buyout plan.

Lorenzo has taken advantage of deregulation in recent years to build an airline empire that already includes Continental Airlines, one of the nation's oldest airlines, and New York Air, an East Coast airline.

Frontier, which is a direct competitor of Lorenzo's company in the Southwestern part of the country, serves an additional 36 destinations that Continental does not serve. This traffic could be used to support Continental's longer haul flights, Texas Air said.

Texas Air said that Frontier would benefit by admission to Continental's frequent flyer program, a multimillion dollar advertising campaign and expansion of a joint fare program begun last year.

Denver-based Frontier, the nation's 15th largest airline founded in 1946, has experienced severe economic difficulties in recent years and has drastically reduced its operations. In 1983, the company reported a net loss of $13.7 million, while last year that loss increased to $31.1 million.

Texas Air began life as Texas International Airlines, a scrappy regional carrier that took advantage of airline deregulation in the late 1970s to grow dramatically beyond its original base in Texas. In 1980, the company formed New York Air to provide service in the eastern half of the United States.

Under Lorenzo's leadership, Texas Air made an unsuccessful bid to take over National Airlines -- later bought by Pan Am -- and then used profits from that attempt to help fund a $200 million buyout of Continental Airlines in 1981, giving the airlines, which took Continental's name but kept its corporate identity, coast-to-coast service.

Lorenzo next tried to acquire TWA in a merger that would have created the nation's second-largest airline, but Texas Air was out-maneuvered by corporate raider Carl Icahn. After the months-long battle this summer for control of TWA, Texas Air agreed to pull out of its merger contract with TWA in return for $51 million in stock profits and other payments.

Texas Air's operations generally have been characterized by tight management and low labor costs. New York Air was set up as a non-union carrier, and Continental stirred a great deal of controversy two years ago by filing for bankruptcy protection to enable it to break high-cost union contracts.

The Texas Air tender offer is scheduled to expire on Oct. 18, and is subject to the condition, among others, that Texas Air's application be approved the Department of Transportation.

Texas Air was up 75 cents yesterday on the American Stock Exchange, closing at 16 7/8, and Frontier, which was not traded yesterday, closed Wednesday at 17 3/8.