A novel robust predictive controller for input-saturated LTV discrete-time systems with polytopic model uncertainties is presented. The solution is based on the minimization, at each time instant, of an upper-bound of the "worst-case" infinite horizon quadratic cost under the constraint of steering the set-valued future state evolutions emanating from the current state into a feasible and positive invariant set. A condition on the initial state is given that suffices to ensure problem solvability for all subsequent time instants. Under the latter, the proposed predictive controller is proved to robustly asymptotically stabilize the input-saturated LTV polytopic system.