After spending four seasons with Radnički Niš, Grujić moved abroad and joined Belgian club Molenbeek in 1995.
[1] Over the next six seasons, Grujić played 146 league games and scored two goals.
He subsequently signed with ADO Den Haag[2] and stayed with the club for two years.
After spending six months without a club, Grujić joined Rad in his homeland during the 2007 winter transfer window.
Grujić made his solo international appearance for FR Yugoslavia in a 2–1 friendly win away against Northern Ireland on 16 August 2000.