Taking buyback contract as an incentive mechanism of supply chain system, the optimal ordering quantity, pricing, and system coordination in a single-supplier single-retailer supply chain under distribution-free environment is investigated. The supplier and the retailer are both risk neutral. Researches on the performance and coordination of supply chain under distribution-free environment are of great importance, especially for new products with insufficient historic sales data, short life cycle products, and products which are difficult to identify the demand distribution by Probability Theory. An upper-bound expected revenue model, a lower-bound expected revenue model and a minimum expected revenue model are established, respectively, for the supplier-retailer supply based on the expected revenue criterion and distribution-free approach. The optimal ordering quantity, pricing decision, and system coordination under the different demand-dependent pricing modes are analyzed. The result shows that the coordination ability of the buyback contract increases as the supply-chain system’s expected revenue changes from the upper-bound expected revenue model to the lower-bound expected revenue model and finally to the minimum expected revenue model. Namely, for the upper-bound expected revenue model, the buyback contract cannot coordinate the supply chain; for the lower-bound expected revenue model, there exists a unique buyback contract; and for the minimum expected revenue model, the buyback contract is a reactive function of the wholesale contract, which can flexibly coordinate the supply-chain system.