2009-10: Jesse Graham skated for the Toronto Young Nationals minor midget team. In 84 games he scored 14 goals with 74 assists. Graham was selected by the Niagara IceDogs in the first round (sixth overall) of the 2010 OHL Priority Draft.
2010-11: Graham played in 63 of 68 games for Niagara in his first OHL season and was part of the gold medal-winning Canada Ontario squad at the 2011 U17 World Hockey Challenge. His plus-27 plus/minus was second only to Dougie Hamilton's plus-35 amongst IceDogs defensemen and he scored 1 goal with 17 assists and had 22 penalty minutes. The IceDogs finished with the OHL's third-best record and were second to Mississauga St. Michael's in the Central Division. Niagara reached the playoff semifinals and in 14 playoff games Graham scored 1 goal with 8 assists and was plus-seven with 8 penalty minutes. In five games at the WHC he had 1 goal with 5 assists and had 2 penalty minutes.
2011-12: Graham attended Hockey Canada's U18 summer camp before returning to Niagara for his second season with the Ice Dogs. He skated in all 68 regular season games for the IceDogs and was a big part of the team's success; Niagara finished first in the Central Division and reached the OHL Finals against the London Knights. Graham finished plus-25 and scored 4 goals with 37 assists while accumulating 36 penalty minutes. In 20 playoff games he was minus-one and had 1 goal with 9 assists and 20 penalty minutes. Ranked 125th in Central Scouting's final rankings prior to the 2012 NHL Draft, he was selected by the Islanders in the sixth round (155th overall).
2012-13: Graham had a big second half offensively in his third season with the OHL's Niagara IceDogs. Over-shadowed by Dougie Hamilton during the NHL lockout, Graham had 2 goals and 19 in the IceDogs' first 50 games. He had seven points in a five-game stretch in late January with Hamilton in Boston and had eight points in seven games in March; finishing the year with 4 goals and 35 assists in 68 games. Graham was -17 with 48 penalty minutes on a Niagara team missing several scorers from the team that reached the OHL Finals. The IceDogs slipped to fourth in the Central Division and lost to Oshawa in the first round. Graham had 3 assists in five playoff games and was an even plus/minus with 6 penalty minutes.
Graham has returned to the Niagara IceDogs for the 2013-14 season.