Abstract: For companies,Carbon Emission Trading Scheme will lead to the changes of their production cost structure and profit mode. Based on game theory,this paper used Cournot model to analyze the competitiveness change of companies with carbon quota constraints,including the output change,the market share change. The effect of carbon quota constraints on the output of the whole industry sector was discussed as well. The carbon intensity difference between companies was highlighted in order to explore the importance of enhancing energy efficiency and reducing carbon intensity. The results show that the company with lower carbon intensity has larger carbon competitiveness that will help the company have advantage of market share at production market. Particularly,with the carbon quota cap becoming tighter,such advantage will get more prominent. The company with higher carbon intensity is more sensitive to the pressure of carbon quota constraint. When the cap is not very loose,the too high carbon intensity may lead to unbearable carbon burden. The most terrible result will be that the company is force to exit the market. From the industrial level,the implementation of emission trading system will make the output reduce to some degree,which raise an important for policy makers,that is,how to find a balance between economy development and carbon reduction.