Distributed multimedia applications are often sensitive to the Quality of Service (QoS) provided by the communication network. They usually require guaranteed QoS service, so that real-time communication is possible. However, searching a route with multiple QoS constraints is known to be a NP-complete problem. In this paper, we propose a new simple and efficient distributed QoS routing algorithm, called "DQoSR," for supporting real-time communication in high-speed networks. It searches a route that could guarantee bandwidth, delay, and delay jitter requirements. Routing decision is based only on the modified cost, hop and delay vectors stored in the routing table at each node and its directly connected neighbors. Moreover, DQoSR is proved to construct loop-free routes. Its worst case message complexity is O(|V|2), where |V| is the number of nodes in the network. Thus DQoSR is fast and scales well to large networks. Finally, extensive simulations show that average rate of establishing successful connection of DQoSR is very near to optimum (the difference is less than 0.4%).