In the presence of uncertainties in the moment of inertia and the external disturbance torque, the nonlinear robust adaptive control law for the control torque and estimation of moment of inertia is designed combining the nonlinear backstepping and Lyapunovo stability. In the control law for the control torque, the nonlinear damping is added to compensate the external disturbance torque, and the globally uniformly ultimately bounded stability of the system is demonstrated. The nonlinear dynamic coefficient is introduced to increase the dynamic performance of the system, shortening the regulating time after fast attitude maneuver. By Matlab/Simulink programming, the simulation of spacecraft attitude manoeuver control is discussed, and the simulation results demonstrate the effectiveness and feasibility of the proposed controller.