A new approach is undertaken to solve the fully fuzzy multiobjective linear programming (FFMLP) problem. The coefficients of the objective functions, constraints, right-hand-side parameters, and variables are of the triangular fuzzy number (TrFN)s. A solution strategy, called compromise solution algorithm (CSA), is presented using a three-step procedure. First, a revised simplex method together with Gaussian elimination in the environment of the linear ranking function is used to convert the FFMLP problems partially into semi fully fuzzy multiobjective linear programming (SFFMLP) problems. Then, the obtained SFFMLP problems are gathered together as a single problem. Finally, the gathered problem is solved by one of four different methods to find a fuzzy compromise solution for the FFMLP problems. The CSA is then numerically applied to a FFMLP problem to illustrate the practicability of the proposed procedure.