The characteristics of cascading dynamics of Internet are analyzed. Different from betweenness centrality, a congestion function to represent the congested extent of node is proposed to assign a dynamic weight to every node. By introducing the concept of “delay time”, the intergradation between permanent removal and nonremoval is built in order to improve the flexibility of the model. A new evaluation function of network efficiency, based on congestion effects, is given in order to measure the damage caused by cascading failures. Finally, based on Statnet and Webgraph topologies the effects of network structure and size, delay time, processing ability and traffic generation speed on congestion propagation are investigated. The congestion propagation process composed of three phases and some factors affecting transition phenomenon are also uncovered.