The fixed charge is the main issue facing by many of the production and transportation systems. It is posing real difficulties in the solving process since it does not depend on the number of units transported in that particular route. Even though the mathematical model has been framed and many of the researchers were done their research, very few were succeed to get the optimal solution. Those methods are effective when the sources and destinations are less in numbers and it is still difficult to get the optimal solution when the number of sources and destinations were increasing. We proposed a method in this paper to solve fixed cost transportation problems based on the linear approximation. It is very easy to understand and not posing any difficulties in the solving process. Using this method we can get a solution which is optimal for the problem in the finite number of steps. Proposed method is effective even though the sources and destinations are large in numbers. © 2020, Research Publication. All rights reserved.