Born in the town of Maikop in 1916 into the family of a railroader, Kostinsky lost his father very early. His mother, a village teacher, encouraged his interest in drawing at a school studio where she taught.

Kostinsky studied at the Rostov-on-Don Art College, from which he graduated in 1939. His first teachers were Chernykh, Neiphel and Oreshkin. After graduating from college, Kostinsky entered the Academy of Arts in Moscow, but was called to military service and studied at a School of Junior Aviation Specialists. Following the War, Kostinsky was appointed Chief Artist of the State Central Museum of the USSR Armed Forces.

In 1950, he was admitted to the Moscow Artists Union, one of the highest honors in Russia, and has been an active participant of Moscow, republic and All-Union art exhibitions. His works have been displayed at foreign art exhibitions in Japan, Sweden, Canada and West Germany.

Kostinsky's sphere of interest is marine landscapes, which reflect different moods of the sea. In his pictures, dedicated to the Baltic Sea, Kostinsky describes sea toilers and their expressiveness with strong and vibrant colors. Also, one of the painter's favorite subjects is trees, as he considers them symbols of nature's grandeur.