Wright began his major junior career with the Vancouver Giants in 2005–06, debuting in two WHL games. The following season, he recorded 12 points in 48 games during his WHL rookie season. He helped the Giants finish as league runner-up in the playoffs to the Medicine Hat Tigers before winning the 2007 Memorial Cup championship against the same Tigers squad in the CHL title final. In 2007–08, Wright improved to 36 points and was drafted 117th overall by the Tampa Bay Lightning in the 2008 NHL Entry Draft. Upon being drafted, Wright continued to play for the Giants, scoring 21 goals and 47 points in 2008–09.