Pro career
Grogan was picked in the fifth round (116th overall) in the 1975 NFL Draft. Grogan holds the record in several New England Patriots' passing categories, including 182 touchdowns. His 16 seasons are the most ever for a Patriots player. He also holds the Patriots single-game record with a 153.9 quarterback rating, achieved by completing 13-of-18 passes for 315 yards with five touchdowns and no interceptions versus the New York Jets on Sept. 9, 1979.

Grogan is noted as one of the top rushing quarterbacks of his time. He rushed for 2,164 yards (4.9 per carry) and 35 touchdowns during his career, a mark which places him as the Patriots' third overall in rushing touchdowns. Those touchdowns also place Grogan tied with Randall Cunningham and Tobin Rote in fourth place all-time among NFL QB's in rushing scores. Steve Young is first with 43 rushing TD's; Kordell Stewart is second with 38; and Steve McNair is third with 37.

In 1976, Grogan led the Patriots to an 11-3 record after the team had finished only 3-11 the previous year. During that season, the Patriots defeated the defending Super Bowl champion, Pittsburgh Steelers, as well as the Oakland Raiders, who would go on to win that season's Super Bowl. Although the 1976 season was not statistically one of Grogan's best, his 12 TD's during the 1976 season still stand as the most rushing touchdowns in a season by quarterback. Those 12 TDs ranked fourth among all players in 1976.

Statistically, Grogan's best season was in 1979, when he completed 206 of 423 passes for 3,286 yards and 28 TDs. In Super Bowl XX, Grogan replaced Tony Eason in the second quarter and went on to connect on 17 of 30 passes for 177 yards and a touchdown in a 46-10 loss to the Chicago Bears. Grogan threw the only touchdown pass for the Patriots in that game. During his pro career, Grogan led the Patriots to the playoffs four times (1976, 1978, 1982, and 1985).