Abstract: Iterative learning control is an effective approach to the control of processes that are repetitive in nature. In this paper, an open-closed-loop PI-type iterative learning control scheme for the precise tracking control of a class of discrete nonlinear time-varying systems over a finite time interval is presented. The scheme updates control input with tracking errors of both current and last iterations simultaneously. Sufficient and necessary conditions which guarantee the convergence of the scheme are given and then proved with inductive method. Finally the conditions are verified with simulation results.