We discuss a new simple method to solve linear programming (LP) problems, based on the so called duality theory and nonnegative least squares method. The success for this method as far efficiency is concerned depends upon the success one may achieve by further research in finding efficient method to obtain nonnegative solution for a system of linear equations. Thus, the suggested method points the need to devise better methods, if possible, of finding nonnegative solution for a system of linear equations. Because, it is shown here that the problem of linear programming reduces to finding nonnegative solution of certain system of linear equations, if and when it exists, and this system of equations consists of 1) the equation representing duality condition; 2) the equations representing the constraints imposed by the given primal problem; and 3) the equations representing the constraints imposed by its corresponding dual problem. In this paper we have made use of well known method of nonnegative least squares (NNLS), [1], as a primary start for finding nonnegative solution for a system of linear equations. Two simple MATLAB codes for testing method by implementing it to solving some simple problems are provided at the end.