Born in Ishinomaki in Miyagi Prefecture, Kosugi first studied at the Nihon Eiga Haiyū Gakkō before joining the Nikkatsu studio in 1925.

He was the lead player in a series of critically acclaimed realist films made at Nikkatsu's Tamagawa studio in the 1930s, particularly Tomu Uchida's Jinsei gekijō (1936) and Tsuchi (1939) and Tomotaka Tasaka's war films, Gonin no sekkōhei (1938) and Mud and Soldiers (1939).

In 1937, he starred in the German-Japanese co-production, Atarashiki tsuchi (aka Die Tochter des Samurai), directed by Arnold Fanck and Mansaku Itami.

He was renowned at the time as a skilled actor with an individual style.

His son was the composer Taichirō Kosugi, who did the music for Cyborg 009.