In this paper, an adaptive neural bounded control scheme is proposed for an n-link rigid robotic manipulator with unknown dynamics. With combination of neural approximation and backstepping technique, an adaptive neural network control policy is developed to guarantee the tracking performance of the robot. Different from the existing results, the bounds of the designed controller are known a priori, and they are determined by controller gains, making them applicable within actuator limitations. Furthermore, the designed controller is also able to compensate the effect of unknown robotic dynamics. Via Lyapunov stability theory, it can be proved that all the signals are uniformly ultimately bounded (UUB). Simulations are carried out to verify the effectiveness of the proposed scheme.