He studied with his father and at the Moscow School of Painting, Sculpture and Architecture at the faculty of Architecture under Abram Arkhipov, Nikolay Kasatkin, Leonid Pasternak, and at studio of Valentin Serov and Konstantin Korovin.

Krymov taught at the Moscow High Artist Technical Workshops from 1920 to 1922 and at the faculty of fine arts of Prechistenka Practical Institute from 1922 to 1924.

He painted chiefly provincial towns and village landscapes, focusing prominently on the countryside.

He was noticeably influenced by primitive folklore, though later his style changed to a more classical approach.

Krymov was awarded the rank of Honorary Art Worker of Russian Federation in 1942, the Order of the Red Banner of Labour in 1954, and the rank of People's Artist of the RSFSR (visual arts) in 1956.