 Dodd married Alice Davis in 1933, and they had two children, Linda Dodd Thompson and Robert Lee Dodd Jr., who played quarterback for the University of Florida during 1960 and 1961 football seasons. Dodd Jr. had wanted to play for Georgia Tech, but Dodd thought it would be best if he played for another college. On October 1, 1960, Dodd Jr. contributed to Florida's 18-17 upset win over the Yellow Jackets at Florida Field with Ray Graves, Dodd's former assistant, as the Gators' head coach.
