As the world's largest carbon resources country with relatively great carbon emission, China in has just started its carbon trade. China is only a passive participant in international carbon trading market, rarely participating in the project of Clean Development Mechanism (CDM). Therefore, trade market of emission permits can be divided into first and second trade markets. During the definition of emission right, we found out that the ways of emission trade at second carbon trade market is the key to the research on carbon trade, which can realize the allocation efficiency and utilization efficiency of resources. Then, feasibility of implementing auction system of emission permits trade in China is analyzed from the aspects of legal protection, technical support, and supervision and management. Chatterton and Samuelson double action model is adopted to determine the market strike price for market clearing. In this auction, a seller and a buyer offer the asking price and bid price for a unit of emission permits, respectively. And the bidding strategy is determined in order to obtain the maximum profit for both seller and buyer. Game Model for carbon emission permits is established. Finally, allocation efficiency of emission permits trade market of carbon is studied and the Nash Equilibrium in this model is analyzed, so as to provide theoretical references for emission permits trade of carbon in China.