Grekov studied at the Odessa Art School, 1898–1903, and at the St. Petersburg Academy of Art. He was a member of the Association of Artists of Revolutionary Russia and from 1931 he lived in Moscow. He was the founder of Soviet battle scene painting and was one of the first artists to address himself to the actual events of the Civil War of 1918–20. His works depicted the battles of the First Cavalry Army and created an image of the people fighting heroically for Soviet power. Most of Grekov's paintings are characterized by historical authenticity of events and types and a truthful re-creation of the whole atmosphere of the Civil War. The Studio of War Artists was named after him.
His paintings include Onward to Budennyi's detachment (1923), Liquidation of the remnants of General Krzhizhanov-skii's army (1924), Tachanka (1925). Trumpeters of the First Cavalry Army (1934), and Budennyi's detachment unmounted is repulsing the enemy's attack (1934), all in the Tretyakov Gallery.