In order to support multimedia communication over high speed networks, it is necessary to develop routing algorithms which use for routing more than one QoS parameter. This is because new services such as video on demand and remote meeting systems require better QoS. However, the problem of QoS routing is difficult and to find a feasible route with two independent path constraints is NP-complete. Therefore, QoS routing algorithms for high speed networks must be adaptive, flexible, and intelligent for efficient network management. In this paper, we propose a QoS routing method based on Genetic Algorithm (GA). The proposed method uses two QoS parameters for routing. The simulation results show that proposed method has a better performance than a routing algorithm with only one QoS parameter and a conventional method.