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This paper develops a two-echelon green supply chain that consists of one green manufacturer and one retailer. The green manufacturer has both online direct and offline retail channels. Considering manufacturer’s risk attitude and product’s green level, the paper constructs centralized and decentralized game models when the online channel’s demand is uncertain. Furthermore, this paper analyzes the impacts of a set of factors, including consumer environmental awareness (CEA), product green level, and risk attitude on decision-making in the supply chain. Finally, we present numerical examples. The main findings are as follows: the manufacturer and the retailer will benefit from the improvement of CEA; hence, they could invest more to obtain more profits by improving CEA; manufacturer’s risk attitude has a negative impact on the pricing and profits of the supply chain; as such, the members of the supply chain should improve the accuracy of their demand forecast, so as to minimize risks and losses resulting from uncertainty in demand.