Abstract: From the perspective of stochastic evolution game, this paper analyzes the game behavior and income changes of local authorities, key emission units and third-party verification agencies in different situations by constructing a game model of carbon verification data quality supervision, and discusses the evolutionary path and evolutionary stability strategy of carbon verification data quality supervision. The results show that the strategy evolution of different subjects under random interference shows differences, and the strategy choice of key emission units shows high stability and adaptability, while the strategy choice of local authorities and third-party verification agencies shows high volatility. The intensity of carbon emission reduction subsidies is the core factor affecting the strategic evolution of local authorities and third-party institutions. It affects the different paths of strategic development of both parties. It is necessary to comprehensively balance the interests of both parties to ensure the coherence and effectiveness of the strategies. The risk cost has obviously evolved in the strategic choices of local authorities and third-party verification agencies. It can strengthen the supervision and accountability system, significantly increase the cost of illegal activities, further restrict the behavior of both parties, and provide a good ecological environment for carbon verification.