Bankston is the son of the late long-term Louisiana Democratic Party chairman Jesse Bankston and the former Ruth Paine (1918–1997). Ruth Bankston was a member of the East Baton Rouge Parish Democratic Executive Committee and was a delegate to two national party conventions. Larry Bankston has a sister, Shirley B. Newsham, and two brothers, Dale Leon Bankston and Jesse Bankston, Jr., an assistant district attorney in East Baton Rouge Parish.
