The accessibility of hospital facilities is of great importance not only for maintaining social stability, but also for protecting the basic human right to health care. Traditional accessibility research often lacks consideration of the dynamic changes in transport costs and does not reflect the actual travel time of urban residents, which is critical to time-sensitive hospital services. To avoid these defects, this study considered the city of Kaifeng, China, as an empirical case, and directly acquired travel time data for two travel modes to the hospital in different time periods through web mapping API (Application Program Interface). Further, based on travel time calculations, we compared five baseline indicators. For the last indicator, we used the optimal weighted accessibility model to measure hospital accessibility for each residential area. The study discovered significant differences in the frequency and spatial distribution of hospital accessibility using public transit and self-driving modes of transportation. In addition, there is an imbalance between accessibility travel times in the study area and the number of arrivals at hospitals. In particular, different modes of transportation and different travel periods also have a certain impact on accessibility of medical treatment. The research results shed new light on the accessibility of urban public facilities and provide a scientific basis with which local governments can optimize the spatial structure of hospital resources.