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A very thin graphene nanoribbon/polyvinyl alcohol (GNR/PVA) composite film has been developed which is light weight and requires a very low concentration of filler to achieve electromagnetic interference (EMI) shielding as high as 60 dB in the X band. Atomic force microscope studies show very well conjugated filler concentration in the PVA matrix for varying concentrations of GNR supported by Raman spectroscopy data. The films show 14 orders of increase in conductivity with a GNR concentration of 0.75% [corrected] in PVA. This is possible because of the interconnected GNR network providing a very low percolation threshold as observed from the electrical measurements. Local density of states study of GNR using scanning tunnelling spectroscopy shows the presence of localized states near the Fermi energy. There are multiple advantages of GNR as an EMI shielding material in a polymer matrix. It has good dispersion in water, the conductive network in the composite shows very high electrical conductivity for a very low concentration of GNR and the presence of localized density of states near Fermi energy provides the spin states required for the absorbance of radiation energy in the X band.