William Brown, 56, a retired special agent with the Federal Bureau of Investigation, died of cancer Dec. 31 at Fairfax Hospital.

Mr. Brown had been a agent with the Bureau of Internal Revenue before transferring to the FBI in 1951. He was assigned to New York City before coming to FBI headquarters here in 1963. He was a lecturer at the FBI's National Academy and helped in the planning and development of the Bureau's National Crime Information Center system. He retired in 1975.

Mr. Brown then became a criminal justice enforcement system coordinator with the Virginia Criminal Justice Services Commission, a position he help at the time of his death.

He was born in Aberdeen, Scotland, and reared in Mount Vernon, N.Y. He earned a bachelor's degree in accounting from the University of Maryland in 1950.

During World War II, Mr. Brown served in the Navy in the Pacific theater.

Survivors include his wife, Renee Denarie Brown, of the homw in Fairfax; four children. Jacqueline Renee Nystrom, of Arlington, William C., of Fairfax, Denise Ann, of West Milford, N.J., and Scott A., of McLean., his parents, William and Henrietta Brown, of Rivera Beach, Fla.; two sisters, Helen Greeley, of Wantagh, Long Island, N.Y., and Majorie Riehl, of Fairfield, Conn., and one grandson.

The family suggests that expressions of sympathy be in the form of contributions to the American Cancer Society.