To examine the correlation between regional economic growth and inter-region transportation costs in China, this study establishes a regional economic growth model embedded with inter-region transportation costs based on the Cobb-Douglas production function. Based on a balanced growth empirical model, this study verifies the correlation by conducting a regression analysis of the panel data of 29 provinces, municipalities, and autonomous regions from 1985 to 2015. The empirical results show that: (1) The per capita GDP growth among the three regions (namely, the eastern, central, and western regions of China) meets a conditional convergence trend, and the decreasing of the inter-region transportation costs increases the convergence speed; (2) The per capita GDP growth is in line with the club convergence trend within each of the three regions; (3) The trend of the output elasticity of the inter-region transportation costs shows that the gradual decrease of inter-region transportation costs has a positive correlation with the narrowing of economic disparity after the year 2000, accelerating "common prosperity" across different regions in China.