Due to social and psychological factors, the COVID-19 pandemic has impacted international trade, dampened consumption globally, and resulted in conservative investment and spending. To stimulate economic recovery while promoting the establishment of a positive consumption awareness among people, enterprises endeavor to enhance competitiveness and expand market share through various means, such as advertising and discounting. With more attention paid to environmentally friendly products, there are greater challenges encountered by green supply chain management. In this study, a green supply chain network problem is analyzed, involving a manufacturer and a retailer. In addition to the construction of centralized and decentralized decision models, two cost-sharing contracts are adopted to reduce promotion costs for the retailer and improve the level of greenery in products. With the help of game theory, equilibrium decisions can be made by solving the models. According to the results of numerical experiment, cost-sharing contracts can effectively improve the level of greenery in products and the profitability of the supply chain, despite the inability to achieve a win–win situation.