The interest relationship among forest governance stakeholders will change with the influence of political, economic, cultural, and other factors. Studying the logical relationship between various stakeholders in the process of forest management is an important measure to adhere to the “clear water and green mountains are gold hills and silver mountains” and implement the concept of green development under the new form. In this paper, the evolutionary game method is used to build a dynamic evolutionary game model, analyze the evolutionary stability strategy and replicator dynamics of the three core stakeholders of government, enterprises, and rural community residents, and calculate the equilibrium stability point. The behavioral strategy selection and evolutionary stability conditions of each game player are analyzed. The results show that the “guidance” of the government is a strong guarantee for the realization of the tripartite equilibrium. The government is in a very active and strong position and needs the guidance of the government to achieve stability. The results show that the “guidance” of the government is a strong guarantee for the realization of the tripartite equilibrium. The government is in a very active and strong position and needs the guidance of the government to achieve stability. Therefore, the government should actively encourage rural community residents to participate in forest management, strengthen the supervision of forestry enterprises, and achieve effective management of forest resources.