This research applies an panel data stationarity and stochastic convergence test developed by Carrion-i-Silvestre et al. (2005), which has the advantage of considering multiple structural breaks and the presence of cross-section dependence in order to investigate the hypothesis that relative emission $CO_2$ per capita stochastically converge for 11 Asian countries from 1971~2007. We find that relative emission $CO_2$ per capita is stationary after the structural breaks and cross-section dependence are introduced into the model. We also investigate whether Environmental Kuznets Curve (EKC) hypothesis exists in 11 Asian countries. For EKC test, using the panel cointegration tests of Banerjee and Carrion-i-Silvestre (2006) and Westerlund and Edgerton(2007), we find that relative emission $CO_2$ per capita and relative GDP per capita are cointegrated. However EKC hypothesis in 11 Asian countries is not supported.