Abstract: The overdose allocation of government carbon emission rights quota caused by enterprise adverse selection in the free allocation of carbon emission rights initial quota has negatively affected the reduction effect and environmental governance. For this question, this paper builds an evolutionary game model between the governments and the enterprises based on the "Replicator Dynamics Equation" and the "Evolutionary Stable Strategy" to study the evolutionary stable strategy of the game and the system, and to analyze the influence of related parameters on the evolution path through the simulation. The results show that when the fine that the government gets from a lying enterprise is less than its regulatory cost, the evolutionary game has a evolutionary stable strategy in which the enterprise lies to the government about carbon emissions and the government doesn't supervise the enterprise. To avoid such unfavorable situation in which adverse selection is unregulated, the government should actively use various means to reduce regulatory costs and increase the intensity of punishment for enterprises that lie about carbon emissions, while strengthening communication with enterprises, so as to realize the reasonable distribution of the carbon emission rights initial quota.