After playing in the lower leagues of FR Yugoslavia, Grozdić joined Obilić in the 1996 winter transfer window, spending the next three-and-a-half years with the club.
He was an integral part of the team that won the national championship in the 1997–98 season.
In the summer of 1999, Grozdić moved abroad and signed with Dutch club Vitesse.
[2] At international level, Grozdić was capped 11 times for FR Yugoslavia.
[3] He made his national team debut in a 3–1 friendly loss away to Argentina on 25 February 1998.