The continuous deterioration of the ecological environment and the increasing scarcity of resources have posed a serious challenge to the survival and development of human beings, and the implementation of green supply chain management (GSCM) in this context is an effective means to ensure the sustainable development of society and the economy. In order to seek the optimal strategy of evolutionary game in the implementation of green supply chain management and explore the influence of environmental regulation intensity and public preference degree on the evolution process of green supply chain management diffusion development, this paper takes the study of green supply chain management diffusion as the core innovation point, and under the premise of environmental regulation, selects the government, the core enterprise, and the public as the participating bodies of green supply chain management diffusion, and uses the theory of evolutionary game to construct a diffusion model of green supply chain management. Using evolutionary game theory to construct a diffusion model, and with the help of MATLAB and other mathematical tools for numerical simulation analysis, we discuss the diffusion of the green supply chain and derive the optimal combination strategy. The results of the study show that: (1) there are four evolutionary stable states in the process of green supply chain management diffusion: preliminary diffusion, extinction, semi-diffusion, and full diffusion; (2) it will be beneficial for the government to promote the evolutionary diffusion of green supply chain management by implementing a higher intensity of pollution tax policy while implementing green supply chain incentive strategies; (3) the government, while implementing environmental regulation policies, should also pay attention to the guidance of the public’s awareness of environmental friendliness and greenness, and focus on the role of the comprehensive strategy selection of the three parties of the game in reaching the optimal state. The conclusions of the study provide theoretical guidance and decision support for the implementation and diffusion of green supply chain management under environmental regulation.