The existing controlled UDP schemes for personal terminal to personal terminal (P2P) at application layer are invalid for the congestions in transport layer since the controlled UDP traffics still block the TCP flows. Thus, it is difficult to achieve the congestion control for the TCP/UDP hybrid traffics network. To solve these problems, C-UDP protocol and new edge router are proposed for hybrid traffics' network. The proposed C-UDP and edge router limit the data rates of UDP subscribers according to router link capacity and route delay, and allocate the link capacities to TCP traffics and C-UDP traffics. The proposed C-UDP AQM algorithms implement fair link capacities of an edge router, being required the edge router to have a independent buffer and C-UDP protocol to support. The proposed C-UDP AQM algorithm achieve the network congestion control by operating AQM parameters on the conditions of proposed theorems for edge router and C-UDP subscribers. The dynamic simulation results demonstrate the proposed C-UDP protocol and edge router for the TCP/UDP hybrid traffics network to be valid.