The spacing between graphene and metal substrates has been investigated using total-reflection high-energy positron diffraction (TRHEPD). The rocking curve analysis performed, based on the dynamical diffraction theory, shows that the spacing between the graphene layer and a substrate of Cu(111) and that between graphene and a Co(0001) substrate are 3.34 angstrom and 2.06 angstrom, respectively. The former is close to the interlayer spacing in graphite, suggesting a weak interaction with the substrate material, whereas the latter value experimentally verifies that, in the case of graphene on Co(0001), there is a strong interaction with the substrate. (C) 2016 Elsevier Ltd. All rights reserved.