A Federal Communications Commission law judge, breaking an eight-year legal logjam, yesterday approved the application of a local black businessman to operate the Washington area's first subscription television station.

The station already has contracted with Teleprompter Corp. to feed it pay television programming. But under FCC rules, subscription television stations also must broadcast 28 hours of free, conventional programming.

The company's majority stockholder, Theodore Ledbetter Jr., the son of a prominent District minister and an engineer and communications consultant here, said yesterday that, barring appeal, he hopes the station can be on the air within a year. Parties, including the commission, have 30 days to appeal the decision.

Ledbetter said he has wanted to bring a new station to the community because the existing stations do an inadequate job of covering local issues.

"Local communications needs are not well served by the existing media here," Ledbetter, 40, said in an interview. "I've wanted to get a television station that can serve the Washington community on a local basis, as a city of people, as opposed to the nation's capital."

Ledbetter said that by offering the part-time pay-TV programming, the film and sports fare of most cable outlets, the new station will be able to afford to offer the public affairs programming he hopes to promote. "By relying on STV (subscription televions station) rather than advertising income, I won't have to worry as much about the ratings," he said.

At various stages in his career, Ledbetter operated a CBS affiliate in St. Thomas, Virgin Islands; worked as a documentary filmmaker; served on the staff of the Urban Coalition and managed a tape-cassette franchise here. In 1972, he was considered by President Nixon for a slot on the FCC.

Subscription stations send a scrambled signal over the airwaves. To receive the signal, the subscriber must have a special home decoder, attached to the television set.

Pay television franchises often have been the subject of considerable controversy within the industry, with broadcasters and some local groups claiming that they ultimately damage so-called free home television service.

Although the fledgling subscription industry is only beginning to take hold in major markets, such stations already are operating in Boston and Los Angeles, for example.

Primarily, Ledbetter said the station will offer its subscription programming by charging a monthly fee but noted that in Los Angeles, by paying an additional fee, about 125,000 subscribers were among the few people who could view last month's Sugar Ray Leonard-Roberto Duran fight in their homes.

The seed money for the Ledbetter's investment was put up by the District of Columbia Investment Corp., a branch of the District of Columbia Development Corp., Ledbetter said. After several transactions, he will own 98 percent of the company's stock, he said.

When the application for the station was first filed, the FCC lmited each market to one of these subscription stations. But the ownership of Channel 20 (WDCA-TV), which has since been purchased by Taft Broadcasting Co., filed a challenge to the Ledbetter bid. It is unclear whether the Channel 20 petition is still alive.

But Ledbetter's attorney, Thomas Schattenfield, then challenged the FCC's rule, and the commission ultimately opened a proceeding on the regulation. Last fall the FCC amended its one-to-a-community rule to allow more than one subscription station if the metropolitan area is served by four or more conventional television stations.

In 1967, the FCC granted a license to Theodore Granik, a long-time Washington attorney and broadcast personality, to operate Channel 50 (WGSP-TV). But the project never got off the ground, despite the fact that it was set to operate the old WRC-TV antenna beside the Sheraton Park Hotel.

The operation filed for bankruptcy in 1971 and has been in the hands of a trustee since. The FCC decision yesterday transferred to Ledbetter that construction permit.

Ledbetter does not have a transmitter or studio facility yet, but he hopes to purchase an antenna off Georgia Ave. NW, currently owned by the District govertnment. In any event, he hopes to get a site in the District for the station.