Roman made his professional debut in the 2005–06 season, in his native Czech Extraliga with his junior club, HC Vítkovice.
During his second season with the Steelers in 2009–10, on 29 January 2010, Roman was signed by the Dallas Stars to a three-year entry-level contract.
In his first professional North American season, Roman appeared in 72 games with Texas, contributing with a career high 22 points.
Marking the end of his NHL aspirations, Roman signed a new contract extension to continue with the Steel on a two-year deal.
With three productive seasons in the Czech Extraliga, Roman signed a two-year contract in the KHL with his draft team, Avtomobilist Yekaterinburg on 13 May 2015.