In a two-stage supply chain composed of one supplier and one retailer, the supply chain coordination mechanism in a fuzzy continuous demand environment is researched. A positive triangular fuzzy number is used to model the external market demand. Using the method of fuzzy cut sets theory, both fuzzy decentralized and centralized decision-making processes are analyzed, and another model of fuzzy return contract is proposed to help coordinate such supply chain. It is shown that in fuzzy environment there exists a unique problem can be solved by providing different tactics for wholesale pricing and return pricing, and the fuzzy expected profit of each actor can be expected to improve in the return contract. Finally, a numerical example is given to illustrate the models and the solution-seeking process.