As a result of rapid advances in communication technology, fiber optics have begun to be adopted in most telecommunication systems 3s an economic choice Due to the trend of evolution toward broadband communication network with fiber optics and electronic devices. the network design problem for broadband communication has been received a great deal of research attention recently. In this paper, we address a topological design problem for broadband local access network with uncertain demands, which has received surprisingly little attention so far. in our problem, we select a set of hubs and links for constructing network expected penalty cost for the amount of undersupplied In addition to the usual cost terms of the fixed demand problem Our problem can be approximated as a mixed 0-1 integer programming problem by using Szwarc’s linear approximation technique. Then the problem is transformed successfully into a version of classical network design model. Some computational experiments for the model and concluding remarks are described.