Koichi Kobayashi was born in Asahikawa, Japan. In 1965, he came to Tokyo to be a disciple of the legendary Minoru Kitani. He studied along with Cho Chikun, Masao Kato, Yoshio Ishida, and Masaki Takemiya. He would go on and marry the daughter of his teacher, Reiko Kitani (1939–1996), a 6-dan who has won the All-Japan Women's Championship several times. Together they had a daughter, Izumi Kobayashi, who is now one of the leading female Go players in Japan. Kobayashi is one of the few Go players who have won more than 1,200 professional games. Kobayashi's rivalry with Cho Chikun has continued for some time and they frequently play against each other.
Two years after joining Kitani Minoru's dojo, Kobayashi was promoted to be a 1-dan professional. His first tournament victory came from the 4th Shin Ei in 1972. In 1976, he won his first major title, Tengen.