He won 18 caps for the Republic of Ireland and scored one goal, a long-range strike against Spain in a Euro 84 qualifier at Lansdowne Road in November 1982.
On 8 March 1978 at Dalymount Park, Dublin, Grimes played in the first ever Republic of Ireland U21 game; he went on to win six under-21 caps, scoring two goals, both from penalty kicks.
Grimes, who played as a defender and midfielder, began his career with junior side Villa United before joining Stella Maris Football club.
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.
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.