In order to provide corresponding suggestions for the establishment and development of China's carbon trading market mechanism, the three-party game model of the competent government departments, carbon emission enterprises and third-party verification institution in the initial allocation of carbon emission rights and the rotation bargaining game model in the secondary carbon trading market are solved and analyzed in this paper. The results show that the competent government departments should improve the review efficiency effectively to reduce cost by outsourcing the review work to universities, research institutes and other scientific research units and increasing punishment for the collusion behavior between the carbon emission enterprises and third-party verification institution. At the same time, the competent government departments should adopt the regular regulatory policies to deal with collusion behavior and reduce the sampling proportion to cut cost of government review. The trading center should directly determine transaction price in combination with the forces of buyers and sellers, and make matchmaking trading directly by selecting the qualified buyers and sellers at the secondary carbon trading market in process of bilateral open bidding.