This paper illustrates a new method to solve the fuzzy goal programming (FGP) problem. It is proved that the FGP proposed by Narasimhan can be solved on the basis of linear programming(LP) model. Narasimhan formulated the FGP problem as a set of $S^{K}$LP problems, each containing 3K constraints, where K is the number of fuzzy goals/constraints. Whereas Hanna formulated the FGP problem as a single LP problem with only 2K constraints and 2K + 1 additional variables. This paper presents that the FGP problem can be transformed with easy into a single LP model with 2K constraints and only one additional variables. And we propose extended FGP :(1) FGP with weights associated with individual goals, (2) FGP with preemptive prioities. The extended FGP has a framework that is identical to that of conventional goal programming (GP), such that the extended FGP can be applied with fuzzy concept to the all areas where GP can be applied.d.