Between 1977 and 1983, Grimes made 107 first-team appearances and scored 11 goals for Manchester United, where he won an FA Cup-winner's medal as a non-playing substitute in the 1983 final against Brighton. He subsequently joined Coventry City for a fee of £200,000. After only one season he moved to Luton Town where he made 117 appearances and scored 4 goals. In 1988, he won a League Cup winners medal, coming on a substitute and crossing the ball to set up Luton's last-minute winning goal as they achieved a shock 3–2 victory over Arsenal to secure the first major trophy in their history.