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We describe the synthesis of acid functionalized graphene (GE) which is grafted to chitosan (CH) by first reacting the oxidized GE with thionyl chloride to form acyl-chlorinated GE. This product is subsequently dispersed in chitosan and covalently grafted to form GE-chitosan. GE-chitosan is further grafted onto polymetanitroaniline (PMNA) by free radical polymerization conditions to yield GE-CH-PMNA. We have characterized the structure of synthesized GE-CH-PMNA composites by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA), scanning electron microscopy, and conductivity measurements. XRD data suggest the strongly crystalline character of the prepared specimen. Our measurement shows that the dielectric constants of these nanocomposites are remarkably enhanced due to interfacial polarization effect. This study demonstrates that functionalized graphene sheets are ideal nanofillers for the development of new polymer composites with high dielectric constant values.