Abstract: The enterprise environmental behavior problem caused by humans has affected the public health and has become an urgent problem to be solved in the world. This issue has become a hot topic to research for scholars at home and abroad.The third-party international environmental auditing can have a potentially significant effect on enterprise green environmental behavior. Based on the above analysis, the third-party international environmental auditing is introduced to become an important concept of promoting the enterprise environmental behavior problem towards ideal state. The paper considers whether the public participates in the supervision of enterprises to join the third-party international environmental auditing and the evolutionary game model of government, enterprises and the public has been built. In different situations, the government, enterprises and the public's evolutionary stabilization strategy; through the case study, the factors affecting the final strategy choice of the three main bodies are analyzed. Based on the hypothesis of limited reason, the evolutionary path and law of the three game subjects are explored and tried to find the approach to improve the enterprise environmental behavior problem is tried to be found, which could be as a reference for further application of government and enterprise procurement decision. The research shows that the government, enterprises and the public influence each other. The choice of government strategies can guide enterprises to join the third-party international environmental auditing, and whether the public participate in the supervision of enterprises to join the third-party international environmental auditing. Whether the public supervises enterprises to join the third-party international environmental auditing influences enterprises to join the third-party International environmental auditing or not. To join the third-party international environmental audit, the final strategy choice of the government, enterprises and the public is not only related to the initial participation proportion of each subject, but also related to the initial participation proportion of the other subjects.It would be very wise for government, enterprise and public to weigh gain and losses of taking responsibility in inappropriate enterprise environmental behavior from an evolutionary perspective. The above results may provide a fresh perspective for government.

Key words: third party international environmental audit, government regulation, strategy options, evolutionary game, environment pollution