He played high school football at Red Bluff High School and college football at Oregon State University. In 1964, as a sophomore, he started at left end for the Beavers, helping to lead the team to the 1965 Rose Bowl. The 1965 Rose Bowl remains Oregon State"s last Rose Bowl appearance.
After the 1966-1967 NFL football season, the Minnesota Vikings traded Fran Tarkenton for four draft picks in the 1967 NFL Draft.
The Vikings used one of the four, a second round draft pick, to acquire Grim. He played with them for five seasons, helping them to the 1969 NFL championship and a Super Bowl IV appearance, before being traded with two other players and two draft picks as a part of the trade to the New York Giants for Fran Tarkenton.
He played with the Giants for three seasons and the Chicago Bears for a season. Grim ended his career, playing with Fran Tarkenton and the Vikings for his final two seasons, helping the team to the 1976 NFC championship and a Super Bowl XI appearance.
Grim ended his career having played in 133 total games.