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.
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.