The problem of finite-time synchronization for chaotic system is proposed. By applying the global sliding mode control technique and selecting the exponential fast terminal sliding mode reaching law, a global sliding mode controller is designed and applied to synchronization of a class of chaotic systems. Aimed at the chaotic system with parameter uncertainties and disturbance, fuzzy basis function network is introduced to on-line estimate the parameter bound. The design scheme eliminates the reaching phase of sliding mode control. The tracking error stays on the sliding mode surface and tends to zero in finite time. To verify the feasibility and effectivness of this control strategy, the synchronization for Duffing chaotic system is illustrated.