Abstract: The problems of gain and convergence analysis in iterative learning control (ILC) are discussed, and a new ILC algorithm with influence function is presented. This algorithm achieves the influence of the previous controlling information on the current controlling via influence function, which forms a nonlinear controller. Convergence analysis is made in discrete linear time-varying (LTV) system with the two-dimension theory, and the results show that the convergence condition of the presented algorithm is the same as that of the traditional ILC algorithms. However, since more efficient previous information is used, the new ILC algorithm has a faster convergence rate and a better controlling performance. The results of two examples are given to validate the effectiveness of the proposed algorithm.