Iterative learning control (ILC) is an effective tool for repetitive systems to achieve perfect tracking tasks on a finite time interval. However, most of ILC results focus on iterative asymptotic convergence, that is the tracking performance can only be achieved when the iterative operation tends to the infinity, which is undesired in practice. Therefore, a backstepping-based finite-iteration tracking control (FITC) method is designed to ensure the finite-iteration convergence (FIC) of nonlinear discrete-time systems (NDTSs). In this work, the definition of FIC of NDTSs is given for the first time. On this basis, a backstepping-based FITC approach for repetitive NDTSs is proposed by employing variable replacement, and the finite-iteration number is derived via difference inequalities. Moreover, the proposed control strategy avoids the causality contradiction from the traditional backstepping technique of NDTSs. Simulation results are used to illustrate the effectiveness of the presented scheme.