Spatial accessibility is a basic decision-making question constrained by spatial distribution situations and infrastructure conditions. The isochrone model can help address this question by applying temporal geography principles to measure by time-costs. The spatial accessibility aiming at POI facilities can be conducted from two perspectives in general: (1) on the supply side, the supplier's service accessibility is analyzed starting from specific POIs; (2) on the demand side, the customer’s service convenience is analyzed starting from any location to get the nearest service. However, most studies focus on the service area of specific POIs from the perspective of supply. There is no enough attention on isochrones from the perspective of demands. To help close this gap, this study conducted the isochrone analysis of POI accessibility from the perspective of service demand, to explore the time cost starting from any place to the nearest service facility. The geometric measure applies the network Voronoi diagram model considering the distance difference from that in Euclidean Voronoi diagram. We first theoretically explained the idea of the isochrone model in terms of service demands, and then detailed the steps to apply the isochrone model. To construct the model, the POI data were firstly matched with road networks. Then a network Voronoi diagram model was developed using hospital POIs and road networks to acquire massive useful sampling points along road networks and to calculate their network distance to their nearest POIs. The isochrone model was finally constructed using the sampling points and their distance properties which reflect space-time accessibility of any place in the city in the demand of medical care to get the most convenient service. The study used the isochrone model to reveal the potential relationships between the space-time accessibility of POIs and road networks. The influence of road levels was also examined in comparison with a weighted network Voronoi diagram model. It was found that the morphology of the isochrones had close association with the distribution of POIs and the connectivity of road networks.