His elder brother, Ilya Burov, is a fellow freestyle aerials skier and has competed at the 2014 Winter Olympics, 2018 Winter Olympics and in the 2022 Winter Olympics.[7][8] The brothers competed at the men's aerials freestyle skiing event in the 2018 Winter Olympics, with Ilya winning a bronze medal in the event while Maxim Burov finished in 15th position.[9] Four years later they competed at the men's aerials freestyle skiing event in the 2022 Winter Olympics, with Ilya winning a bronze medal again while Maxim finished in 16th position.