This paper investigates the control problem of a spacecraft attitude manoeuvrer with external disturbances. Firstly, the spacecraft attitude dynamical model is introduced; then, the tube-based framework is constructed, which includes a nominal system and an error system. Based on that, the control law design would be a two-step process. To start with, the nominal control law is developed via an adaptive dynamic programming technique and a neural network approximation in order to provide a nominal trajectory to the desired attitude. Moreover, based on the nonsingular terminal sliding mode control scheme, the error controller is derived to lead the actual system to track the nominal trajectory and suppress disturbances. The stability of the closed-loop system is analyzed via the Lyapunov approach and the simulation results could verify the effectiveness of the proposed control scheme.