He studied first with his father, artist Gheorghe Baba, then briefly at the Faculty of Fine Arts in Bucharest, but did not finish his studies. The first exhibition was held in 1934 in the city of Beile-Herculane, which gave him the opportunity to continue his studies at the School of Fine Arts in Iasi (1934-38) under Nikolai Tonitsa. In 1939 he was accepted to teach at the same faculty as an assistant, in 1946 as a professor. In 1948, after his debut at a salon in Bucharest, he was arrested, imprisoned in Iasi, the next year, without explanation, was dismissed from his job and sent to Bucharest. Despite a difficult relationship with the Romanian communist government, which considered him a formalist, he managed to make a career as a book illustrator and artist. In 1955 he was allowed to go to the USSR, in the same year he received a gold medal at the international exhibition in Warsaw. In 1956, three of his paintings were exhibited at the Venice Biennale.
In 1958, Corneliu Baba was appointed professor at the Nicolae Grigorescu Institute of Fine Arts in Bucharest. Vladimir Zamfirescu is among his students.
Participated in exhibitions all over the world annually. In 1964, his personal exhibition was organized in Brussels, in 1970 in New York. Since 1963, Corresponding Member of the Romanian Academy of Sciences. However, although he was extremely famous in Romania and, to a lesser extent, in the socialist countries of Eastern Europe, he never managed to achieve comparable prominence in the West.