It was an American Legion baseball game in 1956 where he played for Crystal Springs against Brookhaven that changed that idea.

Grantham was signed to a baseball scholarship at Ole Miss and offered a tryout as a linebacker on the football team.

In the 1960 Sugar Bowl, he caught a touchdown pass, blocked a punt and had a team-leading nine tackles in the 21–0 victory over LSU as revenge for the previous 7–3 loss to them.

In Super Bowl III, he was cited as a key part of calling defensive formations on the field in the stunning upset that the Jets would complete where they held Baltimore to no points until late in the fourth quarter of a 16–7 victory.

The Professional Football Researchers Association named Grantham to the PRFA Hall of Very Good Class of 2014.

[4] Grantham served as color analyst on radio broadcasts for the Jets after he retired, which lasted a year due to trouble with alcoholism, as he had been drinking on a significant basis since high school.

He worked in public relations with First National Bank in Jackson, Mississippi after moving his family back to the state in 1975 and he later was a sideline commentator on Ole Miss radio broadcasts.