The current work intends to develop a Network Simplex Method for solving Minimum Cost Flow problems. Such method consists of a primal Simplex Method adaptation in which specific characteristics of the network underlying the problem are investigated by searching for the optimal solution within a finite number of spanning trees. The optimal spanning tree is iteratively obtained through successive structure improvements in each formed tree. The higher efficiency of Network Simplex lies both in fewer iterations necessary to achieve the optimum and in the higher speed of these iterations. Therefore, it is a powerful method for solving Minimum Cost Flow Problems. Practical aspects of implementing the algorithm will be discussed, as well as the algorithm´s implementation in VBA (Visual Basic for Applications) through a practical instance.