Linear programming problems with fuzzy variables have been investigated by many researchers in the recent literature. Some methods to solve these problems such as the primal simplex method and the dual simplex method, are based on the concept of comparison of fuzzy numbers by using ranking functions. In this paper, We first introduce a new method fuzzy exterior point simplex algorithm for solving fuzzy number linear programming problems, by use of linear ranking function. We state our recently established results and develop the fuzzy exterior point simplex algorithm. Finally, we give an illustrative example.