Aleksei Grishin began his freestyle skiing career at the age of eight after his mother saw a newspaper advertisement recruiting skiers for the sport.

[5] He made his debut at the FIS Freestyle Ski World Cup in the following year, finishing fourth at the Piancavallo event in Italy in December 1997.

[6] In the finals, he moved up one spot and finished eighth behind fellow countryman Dmitry Dashchinsky, who won a bronze medal in this event.

[7] Grishin finished with a silver medal again in the World Cup circuit at Meiringen-Hasliberg in Switzerland in March 1998.

[8] Grishin reached first place at the first stop of the 1999–2000 circuit in Mount Buller, Victoria on 11 September 1999.

[12] He began the 2001–2002 World Cup ski season with an eighth-place finish at Mount Buller.

[14] At the 2002 Winter Olympics in Salt Lake City, he finished first with 251.76 points in the qualification round and advanced to the finals.

[5] He attempted to defend his World Ski Championships title at the 2003 event in Deer Valley, falling just under two points behind Dimitri Arkhipov of Russia.

[17] Returning to the World Cup competition, he finished with a second, tenth, and fourth place, respectively, in the remaining three races.

[19] In the 2004–2005 World Cup season, Grishin started four races, finishing no higher than eleventh place,[5] including the fourth race where he finished at 28th place (out of 35 competitors) on the first day at Lake Placid in January.

Jump 2 elevated his standing to fourth place overall, but behind his fellow countryman Dmitri Dashinski who finished with a silver medal.

[27] In the 2008–2009 circuit, Grishin started with a first-place finish at Adventure Mountain in Changchun, China, but failed to reach the podium in the remaining five races.

[31] Grishin beat the runner-up by 1.2 points in the finals,[31] becoming the first athlete to win a gold medal in the Winter Olympics for Belarus.

[5] In July 2019, Grishin decided to put his 2010 Winter Olympics gold medal up for auction to raise money for a close individual who required a serious medical surgery.

[2] Previously, the medal was on temporary loan and displayed in the Museum of Contemporary Belarusian Statehood in Minsk.

In 2001, he was awarded with the honorary title of Honored Master of Sports of the Republic of Belarus.