This study is concerned with developing a heuristic for the vehicle routing problem(VRP) which determines each vehicle route in order to minimize the transportation costs, subject to meeting the demands of all delivery points. VRP is known 10 be NP-hard, and it needs a lot of computing time to get the optimal solution, so that heuristic are more frequently developed than optimal algorithms. This study aims to develop a heuristic which can give a good solution in comparatively brief time. Finally, the computational tests were performed using the benchmark problems and the proposed heuristic is compared with the other existing algorithms. The result of computational tests shows that the proposed heuristic gives good solutions, in much shorter time, which are not 1% more expensive than the best known solutions, which are same as the best known solutions in the previous researches.