Due to the uncertainty of the market demand in the supply chain, this paper characterized market demand as a fuzzy variable and proposed single-period and long-term contracts to coordinate the two members (supplier and buyer) in the supply chain. Comparison of the effectiveness of the two contracts in-dicates that a long-term contract is more effective than a single-period contract in improving the profit poten-tial of both the total supply chain and each member in the supply chain. This conclusion is useful to the de-cision-maker in supply chains with fuzzy market demand.