According to the theory of abrupt climatic change, the regional economic development process in Jiangsu province since 1978 is divided into three periods in this paper. Then the paper employs urban centrality index and time cost for transportation, instead of the city scale and the distance factor, to modify the original potential model. Based on the grid arithmetic of GIS methodology, the paper points out the ranges of urban economic effect regions (UEERs) for central cities at different rank in Jiangsu province of main years. Accordingly, Jiangsu province can be separated into different rank of urban economic effect regions. Consequently, the characteristics of UEERs in Jiangsu province since 1978 can be summarized as below: (1) the change in spatial structure from South-North to East-West, (2) the expanding tendency to north for UEERs in the south, (3) the emergence of new central cities in southern Jiangsu province. Furthermore, the mechanism of evolution of UEERs in Jiangsu is also analyzed in this paper, and the development of transportation axes, the diversities of economic development level and the disparities among the input of social product factors are the three main reasons.