Abstract Background China is one of the world’s fastest-aging countries. Population aging and social-economic development show close relations. This study aims to illustrate the spatial-temporal distribution and movement of gravity centers of population aging and social-economic factors and thier spatial interaction across the provinces in China. Methods Factors of elderly population rate (EPR), elderly dependency ratio (EDR), per capita gross regional product (GRP pc ), and urban population rate (UPR) were collected. Distribution patterns were detected by using global spatial autocorrelation, Kernel density estimation, and coefficient of variation. Further, Arc GIS software was used to find the gravity centers and their movement trends yearly from 2002 to 2018. The spatial interaction between the variables was investigated based on bivariate spatial autocorrelation analysis. Results The results showed a larger variety of global spatial autocorrelation indexed by Moran’s I and stable trends of dispersion degree without obvious convergence in EPR and EDR. Furthermore, the gravity centers of the proportion of EPR and EDR moved northeastward. In contrast, the economic and urbanization factors showed a southwestward movement, which exhibited an reverse trend compared to population aging indicators. Moreover, the movement rates of EPR and EDR (15.12 and 18.75 km/year, respectively) were higher than that of GRP pc (13.79 km/year) and UPR (6.89 km/year) annually during the study period. Further, the bivariate spatial autocorrelation variation is in line with the movement trends of gravity centers which showed a polarization trend of population aging and social-economic factors that the difference between southwest and northeast directions and exhibited a tendency to expand in China. Conclusions In sum, our findings revealed the difference in spatio-temporal distribution and variation between population aging and social-economic factors in China. It further indicates that the opposite movements of gravity centers and the change of the BiLISA in space which may result in the increase of the economic burden of the elderly care in northern China. Hence, future development policy should focus on the social-economic growth and distribution of old-aged supporting resources, especially in northern China.