An adaptive second-order sliding mode control method based on RBF neural network is proposed for n-DOF robotic manipulators in the presence of external disturbances. First, RBF neural network is used to approximate the model information. Second, by using adaptive technology to compensate the uncertainty, whose prior knowledge about upper bound is not required. In addition, since the proposed control scheme is continuous, the chattering phenomenon is almost completely eliminated. Finally, the stability and finite time convergence of the proposed method are proved by Lyapunov stability theory. Through the simulation of 2-DOF manipulator and 5-DOF manipulator, the effectiveness and superiority of the control scheme are verified.