Abstract: In the research of iterative learning control (ILC), it is usually assumed that the initial states are consistent with the desired states or the initial states are fixed per iteration. By considering the problem that ILC law is difficult to apply to the tracking control for the manipulator under the restriction of initial states, we change the dynamic model of the manipulator system into a lower-order system by reduced-order transformations. For the transformed manipulator system, an open-closed loop ILC algorithm with angle correction term is proposed, which uses the error signal and the deviation of two adjacent error signals to adjust itself. Compared with traditional P-type algorithm, this algorithm makes better use of the saved and current information; while compared with PD-type algorithm, it overcomes the instability caused by the derivative action. Meanwhile, the angle relationship of output vectors is used as a standard to estimate the quality of the control inputs, ``awarding or punishing'' the changing trend of the algorithm. So, a fast convergence speed and excellent tracking effect are both realized. Improved strategies are proposed for the above algorithm when the limitation of each joint rotating angle is considered. Finally, the simulation results verify the effectiveness of the control scheme.