In this work, we explore the possibility of using a heterogeneous Susceptible-Infected-Susceptible SIS spreading process on an airline network to model airport congestion contagion with the objective to reproduce airport vulnerability. We derive the vulnerability of each airport from the US Airport Network data as the congestion probability of each airport. In order to capture diverse flight features between airports, e.g. frequency and duration, we construct three types of airline networks. The infection rate of each link in the SIS spreading process is proportional to its corresponding weight in the underlying airline network constructed. The recovery rate of each node is also heterogeneous, dependent on its node strength in the underlying airline network, which is the total weight of the links incident to the node. Such heterogeneous recovery rate is motivated by the fact that large airports may recover fast from congestion due to their well-equipped infrastructures. The nodal infection probability in the meta-stable state is used as a prediction of the vulnerability of the corresponding airport. We illustrate that our model could reproduce the distribution of nodal vulnerability and rank the airports in vulnerability evidently better than the SIS model whose recovery rate is homogeneous. The vulnerability is the largest at airports whose strength in the airline network is neither too large nor too small. This phenomenon can be captured by our heterogeneous model, but not the homogeneous model where a node with a larger strength has a higher infection probability. This explains partially the out-performance of the heterogeneous model. This proposed congestion contagion model may shed lights on the development of strategies to identify vulnerable airports and to mitigate global congestion by e.g. congestion reduction at selected airports.