By systematically studying the proton selectivity of free-standing graphene membranes in aqueous solutions we demonstrate that protons are transported by passing through defects. We study the current-voltage characteristics of single-layer graphene grown by chemical vapour deposition (CVD) when a concentration gradient of HCl exists across it. Our measurements can unambiguously determine that H+ ions are responsible for the selective part of the ionic current. By comparing the observed reversal potentials with positive and negative controls we demonstrate that the as-grown graphene is only weakly selective for protons. We use atomic layer deposition to block most of the defects in our CVD graphene. Our results show that a reduction in defect size decreases the ionic current but increases proton selectivity.