Belushi, 50, claims in the lawsuit filed Nov. 2 that Newmar destroyed a fence and landscaping at the home in the posh Brentwood neighborhood and repeatedly made defamatory statements about him to neighbors and friends.
The lawsuit also claims that Newmar spied on Belushi's family from her residence and caused a nuisance by playing loud music directed at his backyard.
"Newmar has engaged in a malicious and premeditated campaign to prevent and destroy Belushi's quiet peace," the lawsuit claims.
Newmar had an unlisted telephone number and could not immediately be reached for comment.
Belushi says the actions of the actress who played Catwoman in the 1960s television series "Batman" caused emotional distress and harmed his reputation and career.
Besides $4 million in damages, Belushi is seeking an injunction against the actress and attorneys' fees.