The congestion control problem in a single node network has been solved by the nonlinear feedback control method, which has been proven to be effective and robust for different routers queue size. However, these control models are based on the single layer network architecture, and the senders and receivers are directly connected by one pair of routers. With the network architecture being more and more complex, it is a serious problem how to cooperate many routers working in the multilayer network simultaneously. In this paper, an effective Active Queue Management (AQM) scheme to guarantee the stability by the nonlinear control of imposing some restrictions on AQM parameter in multilayer network is proposed. The nonlinear control can rely on some heuristics and network traffic controllers that appear to be highly correlated with the multilayer network status. The proposed method is based on the improved classical Random Early Detection (RED) differential equation and a theorem for network congestion control. The theorem proposed in the paper proved that the stability of the fluid model can effectively ensure the convergence of the average rate to its equilibrium point through many routers in multilayer network. Moreover, when the network capacity is larger, the proposed scheme can still approach to the fullest extensibility of utilization and ensure the stability of the fluid model. The paper reveals the reasons of congestion control in multilayer network, provides a theorem for avoiding network congestion, and gives simulations to verify the results.