Gas safety is related to public health, public safety and social stability, and strengthening gas safety supervision not only involves safe production, but also is an important part of maintaining social safety. This paper considers the probability of gas accidents and establishes an evolutionary game model between gas companies and government regulatory departments. Based on evolutionary game theory, the evolutionary process of the choice of the main strategy of the two game players is studied, and the evolutionary stable equilibrium of the behavior strategy of gas enterprises and government regulatory departments is compared and analyzed, and the model is effectively analyzed based on numerical simulation. The results show that: ① The evolutionary stability strategy between gas enterprises and regulatory departments is related to the probability of gas accidents, and when the probability of gas accidents is greater than the sum ratio of full investment income and insufficient safety investment compensation, gas enterprises will adopt the safety investment strategy; ② Under the government reward and punishment mechanism, increasing the government's punishment and reward will prompt gas enterprises to adopt safe investment behavior, but increasing the punishment has a more significant impact on the safety investment behavior of gas enterprises than the reward, and at the same time, the increase in punishment and reward strength inhibits the government's strict supervision behavior; ③ When the penalty imposed by the higher level government on the supervision and responsibility of the local government supervision department is greater than the cost of the government department's supervision, it will prompt the local government supervision department to finally choose strict supervision; ④ With the increase of penalties imposed by higher-level governments, the impact on the choice of behavior strategies of local government regulatory departments is significant, but the impact on the choice of behavior strategies of gas enterprises is not significant. The research conclusions provide important decision-making support for government departments to effectively supervise gas safety production.