This paper aims at the problem that design the network of Rig-star type with the minimum cost, which the Ring is composed of the selected nodes(concentrators) among the several candidate nodes on the network and other nodes(terminals) is connected to the Ring by star subnetwork. Especially, we consider the terminal reliability in network design problem. We develop the heuristic algorithm for network design problem to obtain the near optimal(best) solution for problem. We use an add-heuristic method and 2-exchange method in developing the heuristic algorithm.