This paper presents a new training method for fuzzy neural network (FNN) systems to approximate unknown nonlinear continuous functions. Fast terminal sliding mode combining the finite time convergent property of terminal attractor and exponential convergent property of linear system has faster convergence to the origin in finite time. The proposed training algorithm uses the principle ofthe fast terminal sliding mode into the conventional gradient descent learning algorithm. The Lyapunov stability analysis in this paper guarantees that the approximation is stable and converges to the optimal approximation function with improved speed instead of finite time convergence to unknown function. The proposed FNN approximator is then applied in the control of an unstable nonlinear system and the Duffing system. The simulation results demonstrate the effectiveness of the proposed method.