The federal court suit filed in Atlanta alleges Fox Denver staffer Carol McKinley wrongly reported there had "never been any evidence to link an intruder" to the killing of the 6-year-old, who was found beaten and garroted in a remote basement room in her parents Denver home on Dec. 26, 1996.
The story aired on Dec. 27, 2002.
The suit filed by John and Patsy Ramsey seeks at least $2 million in compensatory and $10 million in punitive damages.
Ramsey attorney L. Lin Wood said his clients sought a retraction from Fox last January, the Rocky Mountain News reported.
"Fox lives on its alleged reputation as fair and balanced," Wood said, "and Fox has been anything but fair and balanced, with respect to the JonBenet Ramsey case."
Police said the Ramseys were under an "umbrella of suspicion" but no charges ever were filed and a grand jury ended its investigation without issuing indictments.
The Ramseys have maintained someone broke into their home and killed their daughter. A judge in a libel suit filed against the Ramseys concluded there was ample evidence an intruder and not the parents were responsible for JonBenet's death.