Time-, angle-, and energy-resolved two-photon photoelectron spectroscopy is used to study image-potential states of weakly bound monolayer graphene on the noble-metal surfaces Pt(111), Au/Ir(111), Au/Ni(111), and Ir(100). Binding energies are increased relative to the substrates, and lifetimes are similar for all systems under investigation. The properties of the image-potential states are mainly determined by the graphene layer with reduced influence of the substrate. Substrate-related occupied surface states close to the Fermi level are observed for graphene on fcc(111) substrates.