This paper incorporates the players’ risk attitudes into a green supply chain (GSC) consisting of a supplier and a retailer. The supplier conducts production and determines the green level and wholesale price as a game leader, the retailer sells green products to consumers and determines the retail price as a follower. Equilibrium solutions are derived, and the influence of risk aversion on the GSC is examined. Our results show that, for the centralized GSC, risk aversion lowers the green level and the retail price; while for the decentralized GSC, risk aversion lowers the wholesale price and the retail price, but it may induce the supplier to increase the green level given a large risk tolerance of the supplier. Meanwhile, the risk-averse decentralized GSC may obtain more expected profit than the risk-neutral decentralized GSC. Furthermore, this paper designs a revenue-and-cost-sharing joint contract to coordinate the risk-neutral GSC, and such a contract can improve the risk-averse GSC under specific conditions.