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In this paper, we investigate a solution procedure for a fuzzy linear fractional optimization problem in which the input parameters are considered as convex fuzzy numbers. By applying a specific fuzzy ranking method which is based on the α-cut concept, and according to Charnes and Cooper’s approach of variable transformation, the solution of the original fuzzy linear fractional optimization model is transformed to the solution of at most two semi-infinite linear programs that are dis similar among themselves via a sign in a constraint and in the objective function. An appropriate cutting plane algorithm(CPA) of Fang is uti lized to obtain the optimal solution of the semi-infinite linear programs. Further, the application of our provided algorithm in facility location theory is discussed properly. Finally, an illustrative example is given to clarify the developed solution procedure.