The study was designed to analyze the economic growth convergence from year 2008 to 2015 in 19 coastal and border provinces (districts) in China. To provide a more comprehensive and objective analysis on the economic growth, we collected real GDP per capita of 19 selected provinces in the 8 years, and utilized four distinct methods of econometrics, which are sigma - Convergence, absolute beta - Convergence, club convergence and quantile regression. sigma - Convergence was conducted in Gini coefficient method and Theil index methods. And we used SLM model and SEM model to explore the effect of spatial interaction in beta - Convergence. The results suggests that the economic growth of overall provinces shows the trend of sigma - Convergence, and there exists absolute beta - Convergence in coastal and border provinces. However, there is no co-integration between the two regions. The study is of some importance in the state policy on economic growth.