Baldwin launched a lawsuit against the Bodyguard star, claiming that he was cut out of millions in a deal with the BP oil company.
According to Baldwin, Costner convinced him and his business partner Spyridon Contogouris into selling their shares in a company that made oil-cleansing technology for $1.4 million (£910,000) and $500,000 (£325,000) respectively.
Costner is then alleged to have sold a contract for the technology to BP executives to help clean the Gulf of Mexico spill in 2010, making a reported $52 million (£33 million) in profit.
WENN reports that the 57-year-old actor took to the stand in a New Orleans court on Thursday (June 7) to defend himself, saying: "I'm not just a celebrity. I'm not just a person who opens doors. I've probably invested more money in cleaning up oil spills than anyone in the world."
The Hatfields & McCoys star went on to add that he will continue to oppose the lawsuit, adding: "My name is at stake."