Strengthening carbon emission supervision is an important guarantee for realizing the government's strategic policy of "establishing an economic system with green and low-carbon recycling development". As the main factor of destroying the environment, enterprises bear the responsibility of carbon emission reduction and social supervision. Under the government's control, enterprises participate in carbon emission reduction passively, but smuggling and over-discharge have occurred from time to time. This article analyzes the relevant factors affecting corporate carbon emissions in response to government carbon emissions regulatory issues. From the perspective of third-party supervision, under the consideration of the government, enterprises and third-party supervision subjects, the evolutionary game model of government and enterprises in carbon emission regulation is established. Under the participation of the third-party supervisory body, the limited dynamic strategy choice among the government and the enterprise as well as the evolution trend of the strategic choices of the two parties under different parameters are studied, and the results are simulated by Matlab software. The results show that third-party supervision plays a significant role in the government and enterprise carbon emissions process, and can directly influence the decision-making choices of the government and enterprises. Therefore, strengthening the supervision of third parties can improve the efficiency of government supervision, ease the pressure of government supervision, reduce the cost of government supervision, and urge enterprises to comply with the emission of carbon dioxide. However, the oversight of the third party has weakened the effectiveness of government regulation. Finally, it proposes countermeasures and suggestions for the government to introduce third-party supervisory bodies more effectively.