In order to study the transmission mechanism of flight delays among multiple airports, airports are taken as nodes and routes as edges to form a complex network. By analysing the similarity between the transmission process of infectious diseases and the transmission process of flight delays between airports, drawing on the idea of the classical infectious disease transmission model (SIR), and considering the differences in the transmission of delays between different airports, the concept of airport importance is proposed, and the multi-airport flight delay transmission model is constructed. The simulation results of the multi-airport flight delay propagation process show that in the multi-airport network, the delay propagation effect is different for different initial delay airports and different airport importance, but the delay propagation law remains unchanged. The control of important airports in the network will reduce the peak number of delayed airports, and the peak number of delayed airports in the network will decrease the most when the important airports to be controlled are determined according to the median value. It can be seen that the model can objectively reflect the dynamic process and changing law of flight delay propagation among multiple airports, and can provide theoretical basis for delay prevention and recovery.