Grošek was drafted 145th overall in the 1993 NHL Entry Draft by the Winnipeg Jets. He played 3 years with the Jets and became the first Czech born player to play for the team. He then went to the Buffalo Sabres and played 5 seasons with them. He played 14 games with the Chicago Blackhawks and the played for the New York Rangers. He played for both the New York Rangers for 2 seasons and their AHL farm team, the Hartford Wolf Pack. He last played in the NHL for the Boston Bruins for 2 seasons.