Rick Grimm, a member of the upscale Santa Barbara community, is accusing the Dances with Wolves star of illegally planting trees around his beachfront property.
According to Grimm, the plants have obscured the view of the ocean from his house, which is located behind Costner's home.
TMZ reports that Grimm claims he sent Costner and his wife several unanswered requests, asking them to trim their hedges.
The suit goes on to reveal that Costner, though contractually obligated not to plant trees that obscure Grimm's view, said that he will not "back down" and will "do everything in his power to secure his privacy".
Grimm is demanding that the actor chop down the trees as well as pay $150,000 (£95,000) in damages for loss of enjoyment and $500,000 (£318,000) for damage to his property value.
Costner, 57, recently won a lawsuit launched against him by actor Stephen Baldwin.
Baldwin accused the Bodyguard star of cheating him out of a multi-million dollar deal with the BP oil company, but a judge ultimately ruled in Costner's favour.