Chapman, 61, shot the former Beatles star in New York in 1980. He told the parole board he now accepted his crime was "premeditated, selfish and evil".
But they told him: "In spite of many favourable factors, we find all to be outweighed by the premeditated and celebrity seeking nature of the crime."
His release would "be incompatible with the welfare of society" and "undermine respect for the law", they concluded.
Chapman was sentenced to 20 years to life in jail in 1981 after pleading guilty to second-degree murder.