He was born in Yerevan. In 1945, after graduating from the Panos Terlemezyan Art College, he entered the Yerevan Institute of Fine Arts (1945–1951), where he studied under Ara Bekaryan and Eduard Isabekyan. In 1951 he embarked on his creative career, and in 1953 he became a member of the Union of Artists of the Armenian SSR and was elected to the union's board. In 1961 Grigor Khanjyan was awarded the title of Honored Artist of the Armenian SSR; in 1963 he was elected a corresponding member of the USSR Academy of Arts; in 1963 he became an Honored Art Worker of the Armenian SSR and was elected to the board of the Union of Artists of the USSR. In 1967 he was awarded the title of People's Artist of the Armenian SSR. In 1973 the distinguished artist was elected a full member of the USSR Academy of Arts. In 1982 he was elected a corresponding member of the Academy of Sciences of the Armenian SSR, and later an academician. In 1983 he was awarded the honorary title of People's Artist of the Soviet Union, and in 1991 he became an honorary member of the Russian Academy of Arts. He received State Prizes of the USSR and of the Republic of Armenia, orders and other awards. He died in Yerevan.