Urban air traffic has gradually attracted attention in recent years, which will bring endless vitality to future urban development. An objective and accurate method of assessing vertiport capacity is the basis for the air traffic flow management of UAVs, which plays an important role in improving the efficiency of urban airspace resources. First of all, this paper establishes a theoretical capacity calculation model for ground facilities such as takeoff and landing platforms, taxiways and aprons, respectively. Next, this paper analyzes the service characteristics of each ground facility and establishes different types of UAV queuing systems to obtain UAV delay curves based on a UAV Poisson flow arrival model. Subsequently, a suitable acceptable delay level is selected to obtain the corresponding UAV flow, which means the actual capacity of UAV operations. Eventually, the validity of the model is verified through actual drone data arithmetic examples. The calculation results show that the combination of “1 landing + 2 takeoffs” can achieve better capacity results and that the landing platform is more prone to congestion than the takeoff platform. Change in average service time has the greatest impact on the apron capacity, and the takeoff platform is the most sensitive to changes in the acceptable delay level.