Grahm took part in the selection camp for the Swedish national team at the 2010 Winter Olympics, but failed to make the team, being the last player cut from the roster. She would make her Olympic debut in 2014, scoring 4 points in 6 games as Sweden finished in 4th, losing the bronze medal game to Switzerland. She would score 5 points in 6 games, including her first Olympic goal, at the 2018 Winter Olympics, as Sweden finished in 7th.