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Auction refers to arbitrary resource allocation problems with self-motivated participants: Auctioneer and bidders. Double auction is a kind of auctions with multiple buyers and sellers who trade multiple goods. In double auction each trader submits his bid (price and quantity) to the auctioneer. Then the auctioneer collects all of the bids and tries to assign some buyers to some sellers according to their preferences in a way that the whole of the market reaches its maximum utility, this is called a mechanism. In a traditional double auction market each bid is a linear utility function, but in real world, behavior of buyers and sellers is not linear, therefore we propose a fuzzy non-linear utility function for traders because traders (like all humans) are thinking and making decisions in a fuzzy way. Our aim is to design an optimal double auction mechanism. To find optimum in this non-linear optimization problem, we use particle swarm optimization (PSO).