The fault-tolerant topological design for a computer network leads one to characterize the way in which the nodes are linked to each other with the known connectivity parameter and to the capacity of links, which represent the means of transmission parameters between the vertices. The design problem is to find a suitable fault tolerant network topology at a minimum communication cost under the constraint of an average packet time delay. An approach based on Evolutionary Algorithm (EA) is developed for the network topological design problem. The special construction of a chromosome according to fault tolerant network configuration was designed and the modification of fitness function is proposed. Simulations are studied to support the effectiveness of the proposed algorithm.