In this paper, a new robust Iterative Learning Control (ILC) algorithm has been proposed for linear systems In the presence of iteration-varying parametric uncertainties. The robust ILC design is formulated as a min-max problem usmg a quadratic performance criterion subject to constraints of the control input update. An upper bound of the maximization problem is derived, then, the solution of the min-max problem is achieved by solving a minimization problem. Applying Lagrange duality to this minimization problem results in a dual problem which can be reformulated as a convex optimization problem over linear matrix inequalities (LMls). Next, we present an LMI-based algorithm for the robust ILC design and prove the convergence of the control input and the error. Finally, the proposed algorithm is applied to a flexible link to demonstrate its effectiveness.