In this paper, we propose a new design method to construct the highly reliable ATM network based on the virtual path (VP) concept. Through our method, we can guarantee a network survivability, by which we mean that connectivity between every pair of two end nodes is assured even after the failure, and that quality of service (QoS) requirements of each VC connection are still satisfied. For achieving a reliable network, every VP connection between two end nodes is equipped with a secondary VP connection such that routes of primary and secondary VPs are established on completely disjoint physical paths. Our primary objective of the current paper is that the construction cost of the VP-based network with such a survivability is minimized while the QoS requirement of traffic sources in fulfilled. For this purpose, after all the routes of VPs are temporarily established by means of the shortest paths, we try to minimize the network cost through (1) the alternation of VP route and (2) the separation of a single VP into several VPs, and optionally through (3) the introduction of VCX nodes. Through numerical examples, we show how the increased cost for the reliable network can be sustained by using our design method.