Popov was born in Sofia. He debuted in the FIS Alpine Ski World Cup in 2014. He participated at the 2015 and 2017 FIS Alpine World Ski Championships. On 6 February 2018 he won a bronze medal in the giant slalom at the FIS Junior World Ski Championships. On 18 February he debuted at Winter Olympics where he finished 28th in the giant slalom and did not finish the slalom.
- "Albert Popov Personal Profile". Eurosport. Retrieved 31 January 2015.
- "Алберт Попов ще е знаменосецът ни олимпийския фестивал, церемонията е насрочена за 20.30 ч. българско време". winter sports at topsport.bg. topsport.bg. 25 January 2015. Retrieved 31 January 2015.
- "POPOV Albert – Biographie". data.fis-ski.com. Retrieved 2018-02-25.
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