A power market is a special kind of e-market. In a power market, all trading processes are related to three parties: buyers, suppliers and brokers. A broker acts as middlemen between buyers and suppliers in a trading process. In a power market, how to select a potential supplier for a buyer through a broker based on the buyer’s requirements is a challenging research problem. This paper proposes relaxation strategy with fuzzy constraints for supplier selection. The strategy includes three components, i.e., a supplier selection, a fuzzy constraint relaxation, and a decision making. The major contributions of this paper are that (1) the trading process between buyers and suppliers through brokers is modeled by using fuzzy constraints through the consideration of multiple attributes of the buyer’s requirements as well as potential power suppliers; and (2) a buyer can utilize a relaxation with fuzzy constraints to change its requirements in difficult situations when a broker cannot find any supplier to satisfy a buyer’s requirements. Experimental results show that our approach is successfully applied in a simulated power market.