The penalty type education mode for safety production is lack of systematic and comprehensive education thought, education system and education measures, which leads to frequent safety accidents. To promote the safety education level of China’s coal mining enterprises, in this study, the government, coal mine enterprises and employees are included in the evolutionary game model to explore the game relation and evolutionary path of the decision-making behavior among the three stakeholders in the safety management and education. It is proved by decision-making dynamic replication analysis, strategy evolution stability analysis and numerical simulated experiment verification that: the decision-making behavior of the government, coal mine enterprises and employees is the result of the mutual game playing among the three stakeholders. It is impossible for the government to leave alone the enterprises adopting the penalty type education mode for safety production. The incentive type education mode for safety production takes active education thought, education system, education measures and so on. It has become an effective driving factor to promote safety education level and motivate employees’ safety initiative. When certain conditions are met, the decision-making behavior of three stakeholders of the government, coal mine enterprises and employees can evolve into an ideal state. The evolution process of decision-making behavior of three stakeholders to the ideal state is influenced by many factors. The range of different factors has a differential effect on the convergence rate of the three stakeholders to the ideal state.