Most of researchers use the relaxed transportation problem proposed by (Balinski, 1961) to find approximate solution for the fixed charge transportation problem (FCTP). This approximated solution is considered as a lower limit for the optimal solution of FCTP. In this paper a heuristic approach has been developed to find an approximate solution used as a lower limit for the FCTP which is better than that is found by (Balinski, 1961). The same has been validated by applying the algorithm on 37 examples and testing for the significance of results. The algorithm is based on applying the Vogel approximation method on the relaxed transportation problem. In addition, an illustrative numerical example is given to show the simplicity of applying the proposed approach. Keywords: Transportation Problem, Fixed Charge, Heuristic Methods.