Born in Takamatsu City in Kagawa Prefecture, Inokuma studied at the Tokyo School of Fine Arts from 1922 to 1926 with the Western-style painter Fujishima Takeji (1865-1943). A founder of the Shin-Seisaku Kyokai in 1935 Inokuma traveled throughout Europe in 1940 and made a special trip to visit Matisse, an artist whom he greatly admired. Matisse's influence is apparent in Inokuma's work of the period in its simplified means and use of color (see Portrait of the artist's wife sold in these Rooms, 17 October, 1989, lot 259, and Woman with raised hand sold in these Rooms, 29 March, 1990, lot 55).
Inokuma's paintings became purely abstract when he lived in New York City in the 1950s, before ill health forced him to divide his time between Hawaii and Japan in later years. In 1991 the Marugame Gen'ichiro-Inokuma Museum of Contemporary Art in Marugame City, Kagawa Prefecture, opened with an exhibition featuring the artist's 70-year career.