Partnership is the successful implementation of green supply chain management. Now, supply chain partnership is becoming worse and worse because of the lack of corporate social responsibility (CSR). In order to optimize the supply chain partnership, we study the partner selection from the perspective of corporate social responsibility. We construct a payoff matrix of leading companies and cooperative companies in supply chain, and analyze the game relationship between partner selection of supply chain and fulfilment of corporate social responsibility. Our findings show that partner selection depends on the fulfilment level of corporate social responsibility, and leading companies prefer to cooperate with companies with a high degree of social responsibility in green supply chain. Furthermore, the successful establishment of cooperation can encourage companies to fulfil social responsibility consciously. These findings provide support for green supply chain management in the areas of partner selection, harmonious relationship establishment, and social responsibility fulfillment.