The shortest capacitated path problem is a well known problem in the networking area, having a wide range of applications. In the shortest capacitated path problem, a traffic flow occurs from a source node to a destination node in a certain direction subject to a cost constraint. In this paper, a new approach for dealing with this problem is proposed. The proposed algorithm uses a special way to build valid solutions and an improvement technique to adjust the path. Some numerical experiments are performed using randomly generated networks having 25 - 200 nodes. Empirical results are compared with the results obtained using Genetic Algorithms which is an established technique for solving networking problems.