Based on the perspective of dividing the total QoS requirement of delay bound into local QoS requirements among links along the path, the authors examine the constraint conditions of resource reservation for satisfying end-to-end delay bound, present a new cost function for resource allocation and a method of the resource allocation for the links according to the principle of cost minimization, and give a distributed three-phase resource reservation algorithm in this paper. The purpose is to make the use of network resources more balanced and more reasonable in order that more call requests can be admitted in future. Furthermore, also discusse resource reservation processing for multicast connection establishment to which the method is applied. Finally, the results of simulations for the method are given and the effectiveness of the method is confirmed.