A new fully fuzzy linear programming (FFLP) problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp δ-parametric linear programming (LP) problem. Giving the value of deviation degree in each constraint, the δ-fuzzy optimal solution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict: to improve the values of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to illustrate the proposed method.