2010-11: Anton Lindholm played for the Skelleftea club in Sweden — appearing in three games with the U20 team — and skated in six international games with the Sweden U17 team. He had no points with 4 penalty minutes in his brief stint in the SuperElit league. In 37 regular season games for the Skelleftea U18 team he scored 9 goals with 15 assists and 36 penalty minutes. In seven playoff games he had 2 assists and 4 penalty minutes as Skelleftea reached the quarterfinals before falling to Timra IK. Lindholm scored 1 goal with 6 penalty minutes in six games for the Sweden U17 team.
2011-12: Lindholm appeared in his first Elitserien game with Skelleftea in January; spending most of the season with the club’s U20 team. He had no points nor penalties in his only men’s team game. Lindholm scored 1 goal with 3 assists and was +9 with 20 penalty minutes in 43 regular season games for the Skelleftea U20 team and was minus-2 with 1 assist in three playoff games. He played six games, including two playoff games, with the silver medal-winning Skelleftea U18 team and was minus-1 with no points and 4 penalty minutes.
2012-13: Lindholm skated in two Elitserien games with Skelleftea and was an assistant captain for the club’s U20 junior team. He had no points and 2 penalty minutes in his brief time with the Skelleftea men’s team. Lindholm scored 1 goal with 9 assists and was +14 with 24 penalty minutes during the regular season for the Skelleftea U20 team and was minus-3 with 1 goal and 2 penalty minutes in five games during the SuperElit playoffs. Lindholm played four games with the Sweden U19 team and scored 1 goal with 1 assists while finishing +6 with 4 penalty minutes.
2013-14: Lindholm made his first SHL appearance with Skelleftea in January and saw limited action in three other games before joining the club for good in March and seeing a regular role in the playoffs. In seven regular season games he averaged 7:48 minutes of ice time, did not register a point and was minus-4 with 4 penalty minutes. In 14 playoff games he scored 1 goal with 2 assists and was +7 with 4 penalty minutes; averaging 16:37 minutes of ice time. Lindholm played 39 games for the Skelleftea U20 team and scored 1 goal with 5 assists while finishing +3 with 34 penalty minutes. Not among the 130 international skaters in the Central Scouting final rankings he was selected by Colorado in the fifth round (144th overall) in the 2014 NHL Draft.