Trevor Cann was born in Oakville, ON and he attended Holy Trinity School while playing local rep hockey with the Oakville Rangers. He was considered to be a workhorse type of goalie.
Cann was the youngest goalie selected to attend the Canadian National Junior Selection camp in 2006. He recorded a shutout with 23 saves for Team OHL at the Canada-Russia Challenge in 2006. Also in 2006, he backstopped Canada, including a shutout in the gold medal game against Team USA at the Under-18 Junior World Cup. He was the starting goaltender for Team Canada at the 2007 Under-18 World Championships in Finland. Cann was also named to the Eastern Conference Team for the OHL All-star Classic in 2007. He participated in the 2007 CHL Top Prospects Game.
Cann started with the Peterborough Petes in 2005, he was a fourth round pick in the OHL Priority Selection. The goaltender saw a significant increase in his ice-time that season. The 2007/08 was another long season for the net-minder. Cann posted a 20-28-3 record with the Peterborough Petes in his third season with the team. His 3.59 GAA and .906 save percentage nearly mirrored his stats from last season, but this year he managed to shutout his opponent twice.
Cann had the best season of his OHL career in 2008/09, first going 5-5-0 with Peterborough, then posting a personal best 30-10-1 record with a 2.51 goals against average (personal best) and a .917 save percentage after a move sent him to London. He also combined for a personal best six shutouts this season. It was expected that he would make the jump to the AHL next season and suit up with the Lake Erie Monsters.
Cann was drafted by the Colorado Avalanche in the second round, 49th overall, in the 2007 NHL Entry Draft. On May 11, 2009, he was signed to a three-year entry level contract with the Avalanche. Cann began his professional career in the 2009/10 season, being shuttled between AHL Lake Erie and the Tulsa Oilers of the Central Hockey League. The following year, Cann started five games for the AHL Lake Erie Monsters in November and made two cameo appearances in relief later in the year; spending most of the season with the Tulsa Oilers (CHL). Cann started 7 of 12 playoff games for the Oilers and was 4-3 with a 2.89 GAA and .916 save percentage.
Cann was given the backup goaltender role with the Monsters in the final year of his contract. He posted career high 9 wins and 25 games with the Monsters during the 2011/12 season, however failed to establish himself within the Avalanche system and was not tendered a new contract.
Cann spit the 2013/14 season between the Colorado Eagles and the Florida Everblades of the ECHL. On October 7, 2014, Cann continued in the ECHL in signing a one-year contract with the newly accepted Brampton Beast. In December of 2014, he earned ECHL goalie-of-the-week honours.