Optimal airport slot allocation is a significant means of airport demand and capacity management， and has always been a research focus in the field of air traffic. Existing research mainly considers the constraints of airport capacity and flight operations， and optimizes the allocation of arrival and departure flight slots at a single airport， with the goal of maximizing the use of airport capacity while meeting the needs of airlines as much as possible. With the construction of multi-airport system in China， the contradiction between the airports in the same multi-airport system competing for key airspace resources has become increasingly prominent. Optimizing the slot allocation of each airport individually may result in congestion of flights from different airports at key airspace points， causing flight delays. Taking airport and airspace resources into consideration to optimize flight schedules is one of the keys to improving the utilization efficiency of multi-airport resources. In particular， the rational allocation of flight slots considering inter-airport fairness is critical， but little work has been done. This paper firstly establishes a multi-objective flight slot allocation optimization model considering airport capacity and airspace capacity to realize the optimal utilization of multi-airport system's resources. Then， a comprehensive consideration of the needs of each airport at potential departure conflict waypoints is given to construct a peak demand-based inter-airport fairness index and overall measurement， which take into account the functional positioning of each member airport in the multi-airport system. Finally， the validity and scalability of the model are proved by the actual flight data of the five airports in the Guangdong-Hong Kong-Macao Greater Bay Area， showing that the model proposed can provide critical reference for research on fairness of various stakeholders of the multi-airport system.