A native of Niigata, Abe learned painting as an autodidact. He moved from working in a representational style towards cubism, surrealism, and finally abstract art, making his career a reflection of major currents of 20th century art. In 1937, he published Distance of a Fairy, a collection of his paintings and poems.

In 1939, he was one of the founding members of the Art and Culture Association (Bijutsu Bunka Kyokai). Abe relocated to Rome in 1962, where he died in 1971 at the age of 58. His geometrical compositions also inspired Italian artists such as Lucio Fontana (1899-1968). A retrospective was held in 2001 at the Tokyo Station Gallery.