Ordering on fuzzy quantities have been attracted a wide domains of studies in fuzzy sets theory in the two last decades. In many practical situations as well as fuzzy mathematical programming, it is necessary to the decision makers consider L-R fuzzy numbers according to their aims. But in the most of methods which are presented to order fuzzy numbers, the authors have been considered a special kind of fuzzy numbers such as triangular fuzzy numbers, trapezoidal fuzzy numbers and etc. But as we know the L-R fuzzy numbers as a general kind of these numbers have not been discussed. Hence in this paper, we focus on a general L-R fuzzy number and propose a new approach to order them as an extension of the method which is given by Nasseri in [14]. For validity of the proposed method, we will illustrate this method based on a convenient examples which is appeared in the literature of fuzzy ordering. Furthermore, we emphasize that the proposed method will be useful for evaluating the optimality conditions in the fuzzy primal simplex algorithms and the other related algorithms such as the fuzzy dual simplex algorithm and the fuzzy two phase simplex algorithm, fuzzy transportation models, fuzzy interval linear programming and etc.