A method for computing a feasible solution for systems of linear inequalities is presented in this paper. The main motivation for this work is to search for a strictly feasible solution of the problem. Unfortunately, there is no guarantee that the algrithm would generated a strictly feasible solution. In general, it converges to a feasible solution if the problem is consistent, or to an infeasible solution which identifies the inconsistency of the problem. On the other hand, numerical tests have shown the effectiveness of the algorithm.