This paper considers an economic design problem of a tree-based network which is a kind of computer network. This problem can be modeling to be an objective function to minimize installation costs, on the constraints of spanning tree and maximum traffic capacity of sub tree. This problem is known to be NP-hard. To efficiently solve the problem, a tabu list coupled genetic algorithm approach is proposed. Two illustrative examples are used to explain and test the proposed approach. Experimental results show evidence that the proposed approach performs more efficiently for finding a good solution or near optimal solution in comparison with a genetic algorithm approach.