With the increasing aging of the world’s population, research on the equitable allocation of elderly care facilities has received increasing attention, but measuring the accessibility of community care facilities (CCFs) in rural areas has received little attention. In this study, which covered 7985 CCFs in 223,877 villages, we measured the accessibility of CCFs in rural areas of Hubei Province by using the nearest distance method. Based on the accessibility calculation, the spatial disparities and agglomeration characteristics of spatial accessibility were analyzed, and the correlated variables related to the accessibility were analyzed from both natural environment and socioeconomic aspects by employing a geographically weighted regression (GWR) model. Our results show that 87% of villages have a distance cost of less than 7121 m and 81% of townships have a distance cost of less than 5114 m; good spatial accessibility is present in the eastern and central regions, while poor spatial accessibility is shown in a small number of areas in the west. The results from the clustering analysis show that the hot spot areas are mainly clustered in the western mountainous areas and that the cold spot areas are mainly clustered around Wuhan city. We also observed that area, elevation, population aged 65 and above, and number of villages are significantly correlated with accessibility. The results of this study can be used to provide a reference for configuration optimization and layout planning of elderly care facilities in rural areas.