In many real networks, temporary and fluctuant high load on nodes does not always lead to the complete failure of them. The recovery of nodes’ traffic function and the corresponding cascading congestion phenomenon can be observed. In this paper, we quantitatively associate local node capacity with external network load, and reveal the cascading congestion phenomenon of networks by modeling the traffic recovery behavior of nodes under fluctuant load. A hard traffic recovery model describing the general traffic recovery behavior of nodes and an adaptive traffic recovery model containing a local flow-adjusting strategy are proposed. We apply the two models to artificial networks and real networks. The network cascading congestion process and the limitation of network delivery ability under given node capacity are revealed. A hierarchical and load-dependent distribution of accepting probability is proved to be beneficial for the adaptive traffic recovery model in enhancing the network robustness against cascading congestion. Moreover, the critical node capacity corresponding to the maximal network load can be determined by our models. This function of our models is significant for obtaining the maximal network delivery ability with the lowest cost of node buffer in real applications.