KTLA-TV of Los Angeles said Thursday that Nathan Marlowe and his wife, Cynthia Manzo, allege Simmons responded negatively after Marlowe began video-taping the 60-year-old rocker at The Grove mall.
Marlowe alleges he was videotaping Simmons and asking the rocker about monogamy last Saturday when Simmons lunged at him.
The lawsuit charges Simmons took the camera from Marlowe and attacked and threatened the couple when they attempted to retrieve the device.
Simmons was not arrested or charged in the alleged incident.
KTLA said Marlowe and Manzo are seeking more than $25,000 in damages in the suit. The couple made civil claims of assault, battery and infliction of emotional distress against the rocker.