In this paper, we present a new finite-time robust Iterative Learning Control (ILC) strategy which can guarantee robust stability of the ILC controlled system in presence of model uncertainty as quantified by an additive or multiplicative uncertainty model. The presented finite-time robust ILC controller distinguishes itself from other robust ILC controllers by 1) exploiting non-causality in its control structure and 2) taking into account the finite time span of a single trial. The different steps in the control design and analysis are extensively discussed and illustrated by means of an example.