The executive director of the Fairfax County Economic Development Authority, the agency that angered board members earlier this year by its issuance of tax-exempt bonds to controversial businesses, unexpectedly has announced he plans to resign from his $52,700 a year job.

David A. Edwards, 43, who has headed the Authority since l974, plans to leave his job May l4, l982, according to a prepared statement released by the authority. The authority, which has a staff of l2 and a budget of $943,000, is charged with luring new businesses to Fairfax and is considered one of the county's most important agencies.

Edwards could not be reached for comment, and commissioners of the seven-member authority -- at whose pleasure the director serves -- were tight-lipped about his resignation, which surprised some Fairfax officials.

"The press release speaks for itself," said Authority vice chairman James W. Todd, president of Mobil Land Development Corp. of Reston. He declined further comment.

"Well, you're sure telling me something I didn't know," said John T. Hazel Jr., one of the most influential lawyers and developers in Northern Virginia. "I'm surprised; I hadn't heard anything about Dave leaving."

Two members of the Board of Supervisors who declined to be named said the commissioners had grown increasingly unhappy with Edwards' performance. "You might say," one said, "that they felt the job outgrew the man."

Last March, board members charged that the largely independent authority had abused its power by agreeing to help several businesses, including one owned by New Right direct mail expert Richard A. Viguerie, obtain tax-exempt financing for new office buildings.

Viguerie later withdrew his application for a $7 million industrial development bond the authority had approved.