The increase of flight delays in recent years which resulted from the rapid development of the civil aviation industry have become a worldwide challenge in recent years. Thus, it is of great importance to understand the origin and mechanism of flight delays in the complex socio-technical air traffic systems, a problem that attracted much attention recently [1,2,3]. Here, we apply a comprehensive analysis of the delay distributions and propose a mathematical model that could help to improve the understanding of delay cascades and the accuracy of flight delay predictions.