A new generalized fuzzy hyperbolic model (GFHM) is proposed, which is proved to be a universal approximator. GFHM can be used as identifier for nonlinear dynamic systems and the back-propagation training algorithm is given. The feature of GFHM is that as the number of input variables or (and) fuzzy subsets increases, the number of the unknown parameters of GFHM would increase linearly. Finally, the adaptive fuzzy control scheme is presented, which can guarantee that the closed-loop system is globally asymptotically stable. The simulation results show the applicability of the modeling scheme and the effectiveness of the proposed adaptive control scheme.