In this paper, a robust neural network control scheme for the switching dynamical model of the robotic manipulators has been addressed. Radial basis function (RBF) neural networks are employed to approximate unknown functions of robotic manipulators and a compensation controller is designed to enhance system robustness. The weight update law of the robotic manipulator is based on switched multiple Lyapunov function method and the periodically switching law which is suitable for practical implementation is constructed. The proposed control scheme can guarantee that the resulting closed-loop switched system is asymptotically Lyapunov stable and the tracking error performance of the control system is well reached. Finally, a simulation example of two-link robotic manipulators is shown to illustrate the effectiveness of the proposed control method.