Frederick Frank Brown, 71, a fromer public shool official in Arlington County and Alexandria, died of cancer Tuesday at Mount Vernon Hospital. He lived in Alexandria.

Mr. Brown was assistant director of personnel in the Arlington schools from 1958 until his retirement in 1971. Prior to that, he had served six years as director of instruction and assistant superintendent of Alexandria city schools.

He came to Northern Virginia from Martinsville, Va., where he had been a teacher, principal and assistant superintendent of schools.

Mr. Brown was born in Phoebus, Va. He was a graduate of Randolph-Macon College in Ashland, Va., earned a master's degree from the University of Virginia and took graduate work at the College of William and Mary.

He worked briefly for the Curtis Publishing Co. and then was an assistant cashier with the Old Point National Bank in Phoebus for 10 years before joining the Martinsville school system.

Mr. Brown had served on the board of directors of both the Arlington and Alexandria Education Associations. He had been a vice president of the Virginia Education Association.

He was a past president of the Baltimore-Washington Local Government Personnel Association and a member of the Public Personnel Association.

He was a Mason and a Rotarian and had served on the board of directors of the Arlington County Safety Council. He had been a vestryman of St. Luke's Episcopal Church in Alexandria.

He is survived by his wife, the former Dorothy Johnson, of Alexandria; three sons, Frank L., of Alexandria, Walter F., of East Orleans, Mass., and Thomas P., of Norfolk, Va.; a sister, Dorothy B. Galanor, of Riverdale, N.Y. and three grandchildren.

The family suggests that expressions of sympathy be in the form of contributions to St. Luke's Episcopal Church or the American Cancer Society.