By introducing the coupling theory, taking the elderly service facilities in China from 2017 to 2023 as the research object, the entropy method and the coupling coordination model are used to analyze the spatio-temporal evolution characteristics of the supply and demand of elderly service facilities in China. The results show that the comprehensive evaluation index of supply and demand of elderly care facilities in all provinces are steadily increasing, but there is an obvious trend of regional differentiation. The coupling relationship between supply and demand of elderly service facilities in most provinces has reached a high-level coupling level. However, the coupling coordination between and demand is still at a low coupling coordination level. The spatial and temporal evolution of the coordination degree of supply and demand coupling of elderly care service facilities is obvious, showing a decreasing spatial distribution pattern from the eastern region to the inland. Based on this, governments should allocate elderly service facilities reasonably, and all regions should formulate development strategies for elderly service facilities according to local social and economic status and the characteristics of the elderly, so as to promote the coupling and coordinated development of supply and demand of elderly service facilities.