An adaptive backstepping terminal sliding mode control scheme is proposed for a class of uncertain nonlinear systems in strict-feedback form with unknown nonlinearities. The dynamic surface control is combined with the first steps of backstepping method to design the virtual controller. In the -th step, only one neural network functions approximator is adopted to compensate all the unknown nonlinearities, and a adaptive neural network controller based on global fast terminal sliding mode design is obtained. The proposed controller design approach avoids the explosion of complexity in traditional backstepping design, and improves the convergence rate and steady-state tracking accuracy of the system by introducing approximation errors and adaptive compensation of uncertainty bounds to eliminate the errors of modeling and parameter estimation. By theoretical analysis, all the signals in the closed loop systems are guaranteed to be semi-globally uniformly ultimately bounded. Finally, the simulation results validate the effectiveness of the proposed method.