In this work, we use Graph Theoretic Approach to solve unbalanced transportation problem which is a special class of Linear Programming Problem. We represented the transportation problem as a bipartite graph and solved it iteratively. To illustrate the method, two numerical examples are solved and the obtained solutions are compared with those obtained via Vogel approximation method. The present method yields superior initial basic feasible solution of the problems. Moreover, the present method is found to be very easy to understand; use and implement compared to the Vogel approximation method and can be applied on real life transportation problems by the decision makers.