According to TMZ, Baldwin is suing Costner for unspecified damages over a business deal that he says went wrong.
The actor claims that Costner persuaded him to become a partner in a company which builds machines that separate oil from water.
The lawsuit states that Costner later convinced Baldwin to sell back his shares following the BP oil slick, but he did not disclose that he stood to make millions from the invention.
It is thought that Costner eventually sold the machine to BP for $52m (£33m).
Baldwin said that Costner "schemed" him and that he was "effectively robbed" of sharing in the profits from the sale.
Costner has not commented on the lawsuit.