Some concepts in Fuzzy Generalized Automata (FGA) are established. Then an important new algorithm which would calculate the minimal FGA is given. The new algorithm is composed of two parts: the first is called E-reduction which contracts equivalent states, and the second is called RE-reduction which removes retrievable states. Finally an example is given to illuminate the algorithm of minimization. Some concepts in Fuzzy Generalized Automata (FGA) are established. Then an important new algorithm which would would calculate the minimal FGA is given. The new algorithm is composed of two parts: the first is called E-reduction which contracts the equivalent states, and the second is called RE-reduction which does retrieving states. Finally an example is given to illuminate the algorithm of minimization.