An adaptive back-stepping controller based on least squares-support vector machine (LS-SVM) is developed for precision positioning of robot manipulators that can compensate for dynamic friction and uncertainty in manipulator dynamics and actuator dynamics. Firstly, using cross-validation algorithm to get LS_SVM initial parameters based on offline learning. Secondly, introducing the error of LS-SVM into the adaptive law of the back-stepping control and designing the compound disturbance observer system by adjusting LS-SVM. Last, choosing Lyapunov function in turn based on the compound disturbance observer and the system error and designing the self-adaptive control system based on state feedback and compound disturbance observer. The Lyapunov stability theory is used to prove stability of the proposed control system. The simulation results show that the proposed method has stronger robustness, smaller tracking error and faster response speed than the conventional PD controller.