Grogan spent his collegiate career at Kansas State University, where he started as a quarterback for his junior and senior years. He threw for 2,214 yards, completing 166 of 371 pass attempts, with 12 TDs and 26 interceptions. He ran for 585 yards and six touchdowns on 339 attempts, punted 7 times for 279 yards (a 39.9 yard average) and as a senior caught one touchdown pass of 22 yards. Against Memphis in 1973, he had a 100-yard rushing game.
Grogan was selected in the fifth round (116th overall) in the 1975 NFL Draft by the New England Patriots. Although he would start every game for four consecutive seasons early in his career, his career was also marked by injuries and quarterback controversies, with Grogan competing with other quarterbacks for the starting job. His second through his fifth season were the only times he would start every game in a season. Besides taking the starting job from former Heisman Trophy winner Jim Plunkett as a rookie, Grogan would later face competition from Matt Cavanaugh, Tony Eason, Heisman Trophy winner Doug Flutie, and Marc Wilson. (By the time Wilson came to the Patriots, he had spent several years battling the displaced Plunkett for the starting job of the Raiders.)
In his first season, Grogan played in 13 games out of the then-14 game regular season, starting 7 of the last 8. Grogan threw for 1,976 yards, 11 touchdowns and 18 interceptions. The Patriots finished with a 3-11 record, and traded Plunkett, their starter for the previous four years, in the off-season. (Plunkett would eventually lead the Raiders to two Super Bowl victories.)
For the Patriots 1976 season, Grogan led the Patriots to an 11-3 record and the franchise's first playoff berth since 1963. The eleven wins were the most Patriots wins in a season since the club’s inception. Along the way the Patriots defeated the defending Super Bowl champion, Pittsburgh Steelers (30-27), although they lost the divisional playoffs (24-21) to the Oakland Raiders. Grogan scored 12 rushing touchdowns in 1976, breaking a record of 11 previously held by Tobin Rote and Johnny Lujack. His record would stand for 35 years until broken by Carolina Panthers star Cam Newton's 14 in 2011.
In the Patriots 1978 season, Grogan led the Pats to an 11-5 record, a division title and the organization's first ever home playoff game, a 31-14 loss to the Houston Oilers. The Pats set the all-time single season team rushing record with 3,156 yards (Grogan rushing for 539 yards and 5 touchdowns himself). That record still stands as the most productive rushing team ever in the history of the NFL. It is also the only season an NFL team has had 4 players rush for over 500 yards apiece.
In the early 1980s, Grogan suffered several injuries, and the Patriots drafted quarterback Tony Eason in the first round of the 1983 NFL Draft.
By the Patriots 1985 season, Eason had taken the starting quarterback position and led the Patriots to a 2-3 record initially. Coach Raymond Berry benched Eason for Grogan. The Patriots won 6 straight wins behind their old quarterback, only to lose Grogan when he suffered a broken leg in Week 12 against the New York Jets. Filling in again at QB, Eason and the Patriots lost that Jets game 16-13 in overtime, and relinquished 1st place in the AFC East Division. With Eason's return, the Patriots went 3-2 in their remaining five games. Finishing the season with an 11-5 record, the Patriots earned a wild card berth into the playoffs and eventually reached Super Bowl XX, where they faced the Chicago Bears, who, with their defensive coach Buddy Ryan's "46" defense, had gone 15-1 during the regular season. Eason, who had led the Patriots to victory in the wild card, divisional, and conference playoff games, started the game, but the Patriots could do little against the Bears' defense and Eason went 0-6 in passing attempts; Coach Berry replaced him with Grogan. Grogan went on to connect on 17 of 30 passes for 177 yards, a touchdown, but also two interceptions, in the 46-10 loss. Of little solace was the fact that the Patriots were the only team to score against the Bears in the playoffs that season.
At the time of his retirement, Grogan led the franchise as the all-time leader in passing yards (26,886) and passing touchdowns (182). He is third in passing yards and passing touchdowns behind Tom Brady and Drew Bledsoe. His 16 seasons are the most ever for a Patriots player. He also held the Patriots previous 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 against the New York Jets on September 9, 1979, before Drew Bledsoe posted a perfect 158.3 rating against the Indianapolis Colts on December 26, 1993.
Statistically, Grogan's best season was the Patriots 1979 season, when he completed 206 of 423 passes for 3,286 yards and 28 touchdowns, rushing for 368 yards and 2 touchdowns. His 28 touchdown passes led the league, tied with Brian Sipe of Cleveland, and his rushing yards led the league for quarterbacks.
Grogan rushed for 2,176 yards (4.9 per carry) and 35 touchdowns during his career, a mark which places him as the Patriots' fourth overall in rushing touchdowns. With Grogan, the Patriots made the playoffs five times (1976, 1978, 1982, 1985, and 1986 as a backup). Before Grogan was drafted, the Pats made the playoffs just once from 1960-1974.
Grogan's injuries and his toughness in response to them are also part of his legacy. One sports writer for the main Massachusetts paper, the Boston Globe, wrote of the "Grogan Toughness Meter" in 2003. The writer, Nick Cafardo, gave a partial listing of Grogan's injuries over his 16-year career: "Five knee surgeries; screws in his leg after the tip of his fibula snapped; a cracked fibula that snapped when he tried to practice; two ruptured disks in his neck, which he played with for 1 1/2 seasons; a broken left hand (he simply handed off with his right hand); two separated shoulders on each side; the reattachment of a tendon to his throwing elbow; and three concussions."
During his career with the Patriots, Grogan would play with some other great NFL players, such as Sports Illustrated's "Greatest Offensive Lineman of All Time", John Hannah.
Grogan's high school, Ottawa High School in Ottawa, Kansas has named its football stadium after him.
Kansas State has retired the number Grogan wore for the Wildcats, #11, to jointly honor him and Lynn Dickey, who also wore #11. It is the only number retired by Kansas State. (Grogan wore #14 with the Patriots.)
Grogan was named to the Patriots 35th Anniversary Team in 1994, and was elected into the Patriots Hall of Fame in 1995. He was also elected to the Patriot's All-Decade teams of the 1970s and the 1980s.