Air transport network, or airport network, is a complex network involving numerous airports. Effective management of the air transport system requires an in-depth understanding of the roles of airports in the network. Whereas knowledge on air transport network properties has been improved greatly, methods to find critical airports in the network are still lacking. In this paper, we present methods to investigate network properties and to identify critical airports in the network. A novel network model is proposed with airports as nodes and the correlations between traffic flow of airports as edges. Spectral clustering algorithm is developed to classify airports. Spatial distribution characteristics and intraclass correlation of different categories of airports are carefully analyzed. The analyses based on the fluctuation trend of distance-correlation and power spectrum of time series are performed to examine the self-organized criticality of the network. The results indicate that there is one category of airports which dominates the self-organized critical state of the network. Six airports in this category are found to be the most important ones in the Chinese air transport network. The flights delay occurred in these six airports can propagate to the other airports, having huge impact on the operation characteristics of the entire network. The methods proposed here taking traffic dynamics into account are capable of identifying critical airports in the whole air transport network. Effective transport of air transport system requires an in-depth understanding of the roles of airports in the network. Whereas knowledge on air transport network properties has been greatly improved, methods to find critical airports in the network are still lacking. In this paper, we present methods to investigate network properties and to identify key airports in the network. A novel network model is proposed with airports as nodes and the correlations between traffic flow of as edges. Spectral clustering algorithm is developed to classify airports. Spatial distribution characteristics and intraclass correlation of different categories of airports are carefully analyzed. The analyzes based on the fluctuation trend of distance-correlation and power spectrum of time series are performed to examine the self -organized criticality of the network. The results indicating that there is one category of airports which dominates the self-organized critical state of the network. Six airports in this category are found to be the most important ones in the Chinese air transport network. airports, having huge impact on the operation characteristics of the entire network. The methods proposed here taking traffic dynamics into account are capable of identifying critical airports in the whole air transport network.