This paper presents the limitations of citeku for solving a fully fuzzy linear programming (FFLP) problem. And accordingly to overcome these limitations a new method has been proposed by using the ranking function. We have considered a FFLP problem with mixed constraints where decision variables are represented by non-negative fuzzy numbers. Triangular convex normalised fuzzy sets are considered for the analysis. To illustrate the applicability and efficiency of the proposed method various numerical examples have been solved and obtained results are discussed.