A new design method of a fuzzy sliding mode controller is proposed for a class of uncertain systems with large and unobservable external disturbances. Firstly, based on the principle of fuzzy sliding mode control, global fast terminal sliding mode control is introduced to make the system reach a steady state in a limited time. Then an adaptive disturbance estimation term compensated by the absolute value of the derivative of the Lyapunov function is constructed to conduct an accurate estimation of external disturbances. Furthermore, a double-layer hierarchical and exponential reaching law global fast terminal fuzzy sliding mode controller is proposed. The dynamic quality of the sliding mode surface is adjusted by the exponential reaching law. The controller can quickly converge to a stable state and effectively eliminate the chattering of the controller. Finally, the effectiveness of the proposed method is verified by a simulation example.