Greg Brown was selected 26th overall in the second round of the 1986 NHL Entry Draft by the Buffalo Sabres. He played three years of NCAA hockey with Boston College, where he scored 24 goals and 120 points in 119 games. In 1989 and 1990 he was a finalist for the Hobey Baker Award, which goes to the top player in NCAA hockey.
In 1990-91, Brown played 39 games as an NHL rookie with the Sabres, scoring once and assisting on two others. He also dressed for 31 games with Buffalo's farm team in Rochester, scoring six goals and 23 points. After spending the entire 1991-92 campaign with the Americans in Rochester, Brown got the call from the Sabres to play in ten games for them in 1992-93.
The Pittsburgh Penguins acquired the services of Brown in 1993-94, where he played 36 games, scoring three times and collecting eleven points. The other half of his season was spent in the IHL with the San Diego Gulls.
Brown last played in the NHL with the Winnipeg Jets in 1994-95, when he dressed for nine games with the club. His final NHL totals were; four goals and 18 points.
Brown continued to play professional hockey through the 2000-01 season, the last three seasons with the Cologne Sharks of the German Elite League.