Plans for a 30-story, $60-million hotel and conference center at Seminary Road and Shirley Highway were announced yesterday by the Winkler Companies of Alexandria.

Harold Winkler, chairman of the firm, said the 550-room hotel would be managed by the Radisson Hotel Corp., a Minneapolis firm that operates hotels, inns and resorts around the nation. The complex, to be called the Radisson Mark Plaza, would be built on a 15-acre undeveloped tract owned for years by the Winkler firm. Since World War II, Winkler has developed rental apartment units and offfice buildings in the area.

The proposed project, which requires rezoning from commercial office to commercial hotel use from the City of Alexandria, will be a joint venture of the Winkler Companies and the Carlson Companies of Minneapolis -- the parent group of Radisson Hotel Corp.

Winkler, whose late brother Mark founded the firm in the late 1930s, said plans for the Radisson Mark Plaza include several restaurants, meeting facilities, retail stores, an in-door-outdoor pool, tennis and recquetball courts, and a health club. A 70-suite corporate lodge facility is planned for executives.

Winkler said development plans will be submitted soon to Alexandria city officials ot obtain necessary rezoning and special-use permits.

If approved, construction on the complex is scheduled to begin late this year, with a completion target in 1983. The hotel would be part of the overall Mark Center development that already includes nearly 5,000 apartments, plus commercial and office space.