She is Baki's girlfriend and her mother, Kinuyo Matsumoto, is Baki's landlord. She cares deeply for Baki, but denies when asked. She is disillusioned by Baki's violent life as an Underground fighter and begs him several times to quit. Though she still disapproves, Kozue better understands Baki's resolve after visiting Emi Akezawa's grave site. After Baki's first tournament match, he reveals that he cares for Kozue. She became his love interest in the second series, and makes love with him just before his fight with Yanagi Ryuukou, allowing Baki to become a "full man". It should also be noted that Yujiro Hanma views her as an excellent woman for Baki. Yujiro also states: "that little bastard got the best woman in the world", after she helped Baki cure the poison left by Yanagi.
Eventually she also shows a stronger side to her personality, when she steps between Baki and Yujiro while they were "flirting" during their fight, even scolding them for beating around the bush.