Air traffic flow management has been a major means for balancing air traffic demand and airport or airspace capacity to reduce congestion and flight delays. However, unpredictable factors, such as weather and equipment malfunctions, can cause dynamic changes in airport and sector capacity, resulting in significant alterations to optimized flight schedules and the calculated predeparture slots. Therefore, taking into account capacity uncertainties is essential to create a more resilient flight schedule. This paper addresses the flight pre-departure sequencing issue and introduces a capacity uncertainty model for optimizing flight schedules at the airport network level. The goal of the model is to reduce the total cost of flight delays while increasing the robustness of the optimized schedule. A chance-constrained model is developed to address the capacity uncertainty of airports and sectors, and the significance of airports and sectors in the airport network is considered when setting the violation probability. The performance of the model is evaluated using real flight data by comparing them with the results of the deterministic model. The development of the model based on the characteristics of this special optimization mechanism can significantly enhance its performance in addressing the pre-departure flight scheduling problem at the airport network level.