Designing a network with optimal deployment cost and maximum reliability considerations is a hard problem, especially when the all-terminal reliability is required. For efficiently finding out an acceptable solution, Genetic Algorithms (GAs) have been widely applied to solve this problem. In these GAs, the reliability values could be calculated in their objective functions. In year 2002, an extended network reliability model was proposed which considers the connection important level between each pair of nodes. This paper proposes an approximation algorithm based on Monte Carlo simulation for the new network reliability model. This approximation algorithm can be integrated into GAs to solve the optimal cost reliable network design problem under the extended model.