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He attended Olney High School where as a junior in 1959 he played halfback. The level of talent the team had, allowed them to reach the Texas Class 2A semifinal. In 1960 he replaced Phillip Slater at fullback and lead his team to a second straight semifinal appearance, while earning all-state honors.
He went on to play at the University of Oklahoma for coach Bud Wilkinson. During his junior season in 1963 he was named a consensus All-American, playing both offense (fullback) and defense (linebacker).
He was one of four Sooners stars who missed the 1965 Gator Bowl game against Florida State University. Grisham, offensive lineman Ralph Neely, halfback Lance Rentzel and end Wes Skidgel signed with professional teams before the game, and were ruled ineligible for the contest, which Florida State University won 36–19 on the strength of four touchdown catches by Fred Biletnikoff.
Grisham rushed for 2,404 career yards and eighteen touchdowns in his college career.