A discussion was made on the control of tracking for n joint manipulator systems with initial error. First, corresponding systems were turned into lower order systems by reduction change and then the lower order systems were redesigned, which could eliminate the limitation that the initial state of each iterative must be equal to its ideal value in Kawamura’s method or fixed. Second, a new rapid iterative learning algorithm was proposed to control the transformed system. It made the best of effective information the system had saved and the output could converge to the desired output as quickly as possible. The convergence speed of the algorithm is faster than the P type algorithm and the computation process is easier than the PD type algorithm. Meanwhile, the instability due to differential operation is avoided in the algorithm. Simulation results validate the validity of the scheme and real-time capability of the system is improved.