Francis Henry Kimbrough (June 24, 1904 – February 4, 1971) was an American football player, coach of football and basketball, and college athletics administrator. He served as the head football coach at Hardin–Simmons University (1935–1940), Baylor University (1941–1942, 1945–1946), and West Texas State University—now West Texas A&M University (1947–1957). Kimbrough was also the head basketball coach at Hardin–Simmons from 1936 to 1941, tallying a mark of 29–50. He was the brother of Texas A&M star football player John Kimbrough.