Frank William Simpson (1871 – December 8, 1929) was an American college football player and coach.

He served as the head football coach at the University of Oregon from 1898 to 1899 and at the University of California, Berkeley in 1901, compiling a career coaching record of 15–3–2.

At California in 1901, he coached the Golden Bears to a 9–0–1 record.

Simpson was killed instantly when his car crashed into a tree when he and his wife were returning from a duck hunt hear Alvarado, California in December 1929.

This biographical article relating to a college football coach first appointed in the 1890s is a stub.