As a part of the financial market, carbon emissions trading market, has a certain degree of association with the stock market. By the end of 2017, China will open the national carbon emissions trading market, and therefore the study of this association will attract more and more attention. On the one hand, this article comprehensively examines the overall correlation between the yield of each carbon trading pilot and the stock market by the linear correlation Granger Causality test and nonlinear Granger Causality test. The result is that there is a unidirectional Granger Causality between the yield of the Guangdong, Tianjin Emissions Exchange and Shenzhen New Composite Index, the Hubei Emissions Exchange and the Shanghai Composite Index. And meanwhile, there are unidirectional and bidirectional Granger Causalities between the yield of Beijing, Shanghai, Guangdong Emissions Exchange and the Stock Composite Indexes. On the other hand, by analyzing the prices and yield unbalanced panel data of each emissions exchange and its regional stock markets, found a significant association in the long-term, short-term there.