Gren began playing football at Falu BS in his hometown. There he made his debut in 1982 in the men's team and managed the club to promotion to the Division 3 Södra Norrland. There, too, succeeded in the championship, until the rise of games against Nyköpings BIS of the walkover in the second division was missed. A year later the squadron victory was repeated, and after they had prevailed against Råsunda IS thanks to the away goals rule, the road to the second class was free. However Gren left the club to hire at IFK Gothenburg in Allsvenskan. With the club he became Swedish champion in 1984.
1985 Gren left Sweden to go to Switzerland to Grasshopper Club Zurich. In his first game for the new employer - a cup match against BSC Young Boys - Gren scored four goals. He graduated in the following 14 years, 427 games for the Hoppers, scoring 45 goals. Gren was used in each position at least once (even a few minutes when goalkeeper ) and has in recent years libero and team captain. Until 2000 he remained loyal to the club and was able to win multiple titles. Five times he was Swiss champion four times and succeeded the triumph in the Swiss Cup.
On 26 June 1984, debuted limits in the Swedish national team, as they took in Milan against Italy and was defeated by a goal from Antonio Cabrini in 2 minutes, 0-1. In the following years he was one of the first permanent employees in the selection, before he first disappeared from view by coach Lars Arnesson after his move to Switzerland. On October 14, 1987, he celebrated under Olle Nordin his return to the national team's colors, as they parted 1-1 draw by the West German national selection in Gelsenkirchen Park Stadium. However, he was only irregularly for the national team on the court. Although he was not used in the preparations for the 1990 World Cup, he still belonged to the squad of the national selection to the tournament and came in the 1-2 defeat in the final group game against Costa Rica as a substitute for Tomas Brolin to a tournament use. Until his last mission on 22 April 1992 in Tunisia, he came in a total of 23 games used a scoring was denied him.
After the end of his active career Gren was initially a youth coach at FC Altstetten. A year later he moved to sameness position at FC Winterthur. About the FC Vaduz, his first coaching position in adult football, he returned to the Grasshoppers, where he became the successor of Murat Yakin assistant coach Hans -Peter Latour.
In July 2009, limits laid down his assistant coaching job and took over as general manager in charge of the Danish club Vejle BK, who was relegated to the second class first division. Since the 2012 season, he is coach of Jönköping Södra IF in the Swedish second division Superettan.
- Swiss champion: 1990, 1991, 1995, 1996, 1998.
- Swiss Cup Winner: 1988, 1989, 1990, 1994.
- Ch League: 1995 /96; 1996/97
- 23 x Swedish International
- World Cup 1990 in Italy