The selections for the model orders and the number of controller parameters have not been discussed for many data-driven iterative learning control (ILC) methods. If they are not chosen carefully, the estimated model and designed controller will lead to either large variance or large bias. In this paper we try to use the kernel-based regularization method (KRM) to handle the model estimation problem and the controller design problem for unknown repetitive linear time-varying systems. In particular, we have used the diagonal correlated kernel and the marginal likelihood maximization method for the two problems. Numerical simulation results show that smaller mean square errors for each time instant are obtained by using the proposed ILC method in comparison with an existing data-driven ILC approach. Copyright (C) 2021 The Authors.