He was the interim head football coach at University of Missouri from 1943 to 1945 while Don Faurot, the standing head coach, served in the Navy during World War II.

He compiled a 12–14–2 record including a 40–27 loss to Texas in the 1946 Cotton Bowl Classic.

With Faurot's return in 1946 Simpson reverted to his pre-war position as an assistant football coach.

[1] Simpson died of a heart attack, on April 20, 1970, at his home in Green Valley, Arizona.

[2] He was the younger brother of hurdler and track coach Robert Simpson.