A local developer who successfully built market-rate apartments in the Catholic University area five years ago has proposed constructing a similar project with its own small shopping center on Michigan Avenue.

The D.C. Board of Zoning Adjustment will hold public hearings next week on the plans of developer Joseph F. Horning Jr. to build 192 garden apartments on an 8.4-acre wooded area across from Trinity College in Northeast.

Horning, one of the city's few major developers who builds outside the city's wealthy upper Northwest neighborhoods, said building apartments in Northeast was a "risk" five years ago, when he built The Heights, a 323-unit garden apartment complex on Taylor Street NE about five blocks from the proposed project.

But The Heights has maintained a 95 percent occupancy rate, and Horning said that convinced him that the community needed more apartments for professionals who can afford apartments that rent for more than $500 a month.

"The supply of apartments in this city is very limited," said Horning, "but from the looks of things there is a broad range of people looking for rental housing."

The Heights was the only market-rate apartment project built in the District between 1980 to 1983, according to Art Goldstein, an official of the Washington area office of the U.S. Department of Housing and Urban Development.

Last year, a total of 401 market-rate apartments were built. The largest was a new section at McLean Gardens on Wisconsin Avenue NW.

At Horning's new project, called Trinity, rents will range from $550 for one-bedroom units to $720 for three bedrooms. Tenants will pay their own utilities.

The new project will include a minishopping complex -- another feature taken from The Heights. Both apartment projects are in one of the city's largest residential communities and are more than mile from a shopping area.

Helen Mitchell, chairman of the Advisory Neighborhood Commission for the area of the project, said, "After he Horning showed us his presentation, everyone who attended the meeting just accepted the plan without any opposition. They like The Heights, and the new project appears to be very similar," she said.

Horning purchased the site at Michigan Avenue and Franklin Street NE from Trinity College for $11 million. The site is now zoned to allow apartment construction, but all new multifamily projects must be approved by the Board of Zoning Adjustment to assess any possible impact on city services.

The site is adjacent to Park Place, a condominium project that was halted after 108 homes were built because of high interest rates that hit the housing market a few years ago. The project was proposed to have 541 stacked town houses.

Horning is quick to point out why be believes that his apartments will succeed even though the condominiums did not.

"Those Park Place are for sale, and ours will be for rent," he said. "Their monthly mortgage is over $1,000, and our rent will average just half that amount." Horning said that the two projects appeal to two very different parts of the housing market.

Construction is scheduled to begin on the apartments in December with completion slated in early 1987, but rental applications will be accepted starting next summer, Horning said. With their completion, Horning said, he hopes to build more apartments on the 25 acres of wooded land behind the proposed Trinity complex.

"I know the city well, and every indication I have says that the market is strong enough . . . so why not?" he said.

The D.C. Zoning Commission will hold hearings Nov. 14 on a request from Horning to rezone a small portion of the current site to allow the shopping area.