In this paper, a novel generalized fuzzy hyperbolic model (GFHM) is proposed. First, the definition of the GFHM is proposed and the approximation capability of the GFHM is discussed. The GFHM is proved to be an universal approximator by Stone-Weierstrass theorem. Further, this fuzzy model is used as identifier for nonlinear dynamic systems and the back-propagation training algorithm is given. Finally, the adaptive fuzzy control scheme based on the GFHM 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.