The development of a multi-airport logistics system (MLS) is closely linked to factors such as regional economy, international and domestic trade, competitive synergies between airports, and the impact of unforeseen events such as the COVID-19 outbreak. There are various causal relationships and feedback loops within the MLS, and it is always in a dynamic state of change, so it is ideal to use a system dynamics model to depict the MLS. Taking the Jing-Jin-Ji MLS as an example, a system dynamics model consisting of an economy subsystem, a trade subsystem, and an airport cluster subsystem is constructed, and the sustainable development of the MLS is studied by simulating three pandemic scenarios with different impact levels. At the same time, different policy simulations and sensitivity analyses are used to find effective strategies to enhance the sustainable development of the Jing-Jin-Ji MLS. The results can provide an effective method for forecasting air cargo volumes in the MLS under the COVID-19 pandemic and provide a basis for the relevant departments to formulate policies for the development of the MLS.