A new functionalised graphene sheet (FGS) filled poly(dimethyl)siloxane insulator nanocomposite has been developed with high dielectric constant, making it well suited for applications in flexible electronics. The dielectric permittivity increased tenfold at 10 Hz and 2 wt.% FGS, while preserving low dielectric losses and good mechanical properties. The presence of functional groups on the graphene sheet surface improved the compatibility nanofiller/polymer at the interface, reducing the polarisation process. This study demonstrates that functionalised graphene sheets are ideal nanofillers for the development of new polymer composites with high dielectric constant values.PACS: 78.20.Ci, 72.80.Tm, 62.23.Kn.