QoS (Quality of Service) routing is a key network function for the transmission and distribution of digitized audio/video across next-generation high-speed networks. It has two objectives: finding routes that satisfy the QoS constraints and making efficient use of network resources. The complexity involved in the networks may require the consideration of multiple constraints to make the routing decision. In this paper, we propose a novel approach using fuzzy logic technique to QoS routing that allows multiple constraints to be considered in a simple and intuitive way. Simulation shows that this fuzzy routing algorithm is efficient and promising.