Recent experimental reports on in-plane proton conduction in reduced graphene oxide (rGO) films open a new way for the design of proton exchange membrane essential in fuel cells and chemical filters. At high humidity condition, water molecules attached on the rGO sheet are expected to play a critical role, but theoretical works for such phenomena have been scarcely found in the literature. In this study, we investigate the proton migration on water-adsorbed monolayer and bilayer rGO sheets using first-principles calculations in order to reveal the mechanism. We devise a series of models for the water-adsorbed rGO films as systematically varying the reduction degree and water content, and optimize their atomic structures in reasonable agreement with the experiment, using a density functional that accounts for van der Waals correction. Upon suggesting two different transport mechanisms, epoxy-mediated and water-mediated hoppings, we determine the kinetic activation barriers for these in-plane proton transports on the rGO sheets. Our calculations indicate that the water-mediated transport is more likely to occur due to its much lower activation energy than the epoxy-mediated one and reveal new prospects for developing efficient solid proton conductors.