A member of the "Ole Miss" Athletic Hall of Fame, he was a linebacker of the University of Mississippi who came to the New York Titans in the 1960 college draft and helped form the backbone of a New York Jets defense that reached the playoffs in 1968 and 1969, and captured the 1968 American Football League and World Championships.
From his right outside linebacker spot, Grantham wrought havoc on opposing offenses. One of the Jets leading tacklers, he was named to the AFL All-Star team five times and played in eight league All-Star games. He was selected to the All-Time All- AFL second team.
He is one of only twenty players who were in the American Football League for its entire ten-year existence, and only seven AFL players who played their entire careers in one city. Grantham is a member of the All-time American Football League team, and a member of the American Football League Hall of Fame