Local access networks (LAN) are commonly used as communication infrastructures which meet the demand of a set of users in the local environment. Usually these networks consist of several LAN segments connected by bridges. The topological LAN design bi-level problem consists on assigning users to clusters and the union of clusters by bridges in order to obtain a minimum response time network with minimum connection cost. Therefore, the decision of optimally assigning users to clusters will be made by the leader and the follower will make the decision of connecting all the clusters while forming a spanning tree. In this paper, we propose a genetic algorithm for solving the bi-level topological design of a Local Access Network. Our solution method considers the Stackelberg equilibrium to solve the bi-level problem. The Stackelberg-Genetic algorithm procedure deals with the fact that the follower's problem cannot be optimally solved in a straightforward manner. The computational results obtained from two different sets of instances show that the performance of the developed algorithm is efficient and that it is more suitable for solving the bi-level problem than a previous Nash-Genetic approach.