The variation in localized surface plasmon resonances of single Au nanodisks (diameter 100 nm and height 25 nm) on 0-13 graphene layers is investigated using dark-field scattering spectroscopy to obtain the graphene electric field screening length. For nanodisks (NDs) with and without underlying graphene layers on a SiO2 (300 nm)/Si substrate, the plasmon resonance red shifts from 604 to 620 nm with increasing graphene layers. The spectra of the plasmonic nanostructures obey an exponential saturation function versus increasing number of layers of graphene from 0 to 13. As a conducting film, the graphene layers screen the electric field generated by the plasmonic resonance of the Au NDs in the vicinity of the interface, and the red shifts of the resonance wavelength are explained in the framework of the electromagnetic field coupling between in-plane antiparallel image dipoles in the graphene layers and the ND dipole. A screening length of 1.2 ± 0.2 nm, equivalent to 3-4 graphene layers, is experimentally obtained, in good agreement with the measurement by field-effect transistors and theoretical calculation in doped graphene. The resonance shift of plasmonic nanostructures on a layered graphene system provides an alternative and convenient method for screening length measurement of graphene films.