Eastern Airlines made a surprise bid yesterday to acquire National Airlines for about $425 million, an offer that bests Pan American World Airways' bid by $9 a share.

Eastern's move further complicates an already complex situation, coming just as hearing by the Civil Aeronautics Board are drawing to a close on competing applications from Pan Amand Texas International Airlines to take over National.

Eastern had opposed the merger proposals of the other two carriers during the CAB hearings, but decided to enter the bidding itself last week after a National official testified that the airline was prepared to entertain higher offers than Pan Am's. National has been opposed to the TXI offer all along.

The Eastern offer is subject to certain waivers from its lenders, resolution of the necessary financial arrangements and the approval of both the CAB and President Carter. As a procedural matter, Eastern also hopes to persuade the CAB to consolidate its proposal with the others and rule upon it at the same time, a proposition that would most likely require a delay in the board's March decision target date.

Antitrust lawyers raised the possibility that an Eastern-National combination could be very vulnerable to an antitrust challenge since the two airlines compete directly on 16 routes, including the well traveled Northeast-Florida market.

Nevertheless, despite the difficulties, Eastern President Frank Borman was optimistic yesterday. "I think we'll have trouble, but we think it can be cone, and our Washington counsel thinks it can be done." he said in a telephone interview.

If Eastern is allowed to buy National, Borman said he expected the CAB would put new airlines on the routes on which they compete. With airline deregulation a fact, he said, other carriers can and in some cases already have aggressively entered the East Coast-Florida arena and other routes as well. Borman said the administration was sending out a signal and "we got the message.

"The airline business is more like any other business now," he said.

Although Eastern was near financial disater just a few years ago, 1978 will be its most profitable year, and Borman says he has "some money" and a "sound financial plan" to accomplish the acquisition.

Pan Am and TXI between them already own 42 percent of National's stock. TXI has of National's outstanding shares at an average price of approximately $27.45, while Pan Am now holds almost 19 percent, purchased at an average price of about $34.32.

Meanwile, National last week scheduled a shareholders' meeting for Jan. 15 to take up the Pan Am offer.

Yesterday, a spokesmn for L. B. Maytag, National's chairman, said no comment could be made on Eastern's unsolicited offer until it was "fully studied and considered."

William T. Seawell, Pan Am chairman and chief executive officer, said a detailed comment will come after study of the Eastern proposal. "But on the face, it is obviously anticompetitive," he said.

TXI Vice President Jim O'Donnell said TXI had no immediate comment but is "carefully studying the most recent developments."