In this study, a two-echelon supply chain is analyzed where the supplier sells the products to retailer, who in turn sells the product to end customers. In such an arrangement, the supplier and the retailer aim to increase their profits individually which causes double marginalization. Several studies have been proposed by researches to solve the problem of "double marginalization'' and its consequences to supply chain performance. Therefore, contractual agreements as coordination mechanisms were developed to improve the supply chain performance. In the literature, many studies have been conducted on these coordination mechanisms under probabilistic demand. However, in the absence of the historical data it is not possible to establish the probability distribution. In such cases, the fuzzy set theory which is another illustration of uncertainty can be used to model the supply chain. In this study, different configurations of buyback contracts on supply chain performance under fuzzy environment are analyzed. Initially, closed-form solution to buyback contract model with fuzzy demand is proposed by using credibility theory. After that, the closed form of this model with fuzzy buyback rate parameter is obtained. And then the effects of the different configurations of the buyback contract model are analyzed by changing the buyback rate and buyback price. Finally, numerical examples are presented to demonstrate the solving processes of the models and the different effects of buyback rate and buyback price on parameters of buyback contract and the fuzzy expected profit value of all members in supply chain.