Real-time communication services will be one of the most promising future applications in both the B-ISDN and Internet. In addition, real-time traffic usually utilizes a significant amount of resources while traversing the network. Thus there is the need for routing mechanisms which are able to satisfy requirements of both real-time traffic and efficient management of network resources. In this paper, firstly we discuss an issue of routing of real-time traffic subject to each end-to-end delay constraint and a path cost. Then, we describe a key concept which is taken into consideration of the requirements simultaneously. Based on the requirements, a delay-constrained least-cost path problem is formulated. Since the problem is NP-hard, a heuristic method is proposed to solve the problem. The heuristic method can always find a delay-constrained path between a source node and a destination node, if there is such a path. Based on the heuristic method, an outline of the synthesis method for Delay-Constrained Least-Cost Path Routing Protocol is also presented.