The Montgomery County government bought an 11-acre estate near a future Metro subway stop on Rockville Pike yesterday as the site for an elaborate multipurpose arts and civic center that would be the first of its kind in the Washington suburbs.

The Center, planned for completion in 1984 at a total cost of $5 million, including the $1.2 million cost of the land, would benefit the arts and artists in the county, rather than to compete with the Kennedy Center or the Wolftrap Center for the Performing Arts.

The project was hailed as "the beginning of a dream" yesterday by Eliot Pfanstiehl, coordinator for the arts at the county's recreation department, who noted that members of numerous local cultural and arts groups have pushed since 1960 for such a comprehensive facility.

"It's a statement that the arts are alive and well in Montgomery County," Pfanstiehl said.

The center's planners expect to make effective use of existing topography in constructing an outdoor amphitheater and to use the mansion that stands on the land overlooking Rockville Pike. Called the Corby Mansion, the structure was built early in this century by Charles I. Corby, a wealthy bakery owner.

The site between Strathmore Avenue and heavily traveled Rockville Pike just 750 feet north of the future Grosvenor Metrorail stop is easily accessible from the Capital Beltway and Interstate Rte. 270.

County Executive James P. Gleason said he wanted to take steps to insure that the arts center got under way before his term in office ends in November. He said the facility is not meant as competition to the existing theaters and concert halls in the area. Rather, it will provide a centralized forum for the county's numerous artistic groups.

"When you look at the statistics, the people who go to the Kennedy Center, to Wolf Trap and to the National Theater are in the majority people who come from Montgomery County . . . We can't build large places like that. The District and Fairfax got there first," Gleason said. "Our primary interest is in training and helping our young people perform."

According to a 1975 study by the consulting firm of Barton-Aschman Associates Inc., there are at least 43 performing arts groups, 16 groups dedicated specifically to the visual arts and 35 civic organizations involved in promoting art and cultural activities in the county. The study said, however, that those figures are conservative since 39 percent of the groups polled did not respond to the survey.

Most of the plans for the peforming arts will be based on recommendations made in the Barton-Aschman study.