Nanocomposite material for power cable insulation has been under extensive research for quite a long time. Advanced organic and inorganic nano filler of metals and non metals with conductive, semi-conductive and insulating inheritance were wide options. The authors prepared and investigated nanocomposite samples made with low density polyethylene as base resin with several nanofillers including nanofiller graphene oxide. In this paper mainly the graphene oxide nanocomposites are presented. The volume resistivity measurements were performed. The dielectric spectroscopy measurements were made under high and low electric stress, wide range of frequency and temperature, the parameters such as conductivity, real and complex permittivity were observed. The frequency sweep of the 0, 0.1, 0.5 phr samples under different temperatures disclose the variation in dielectric loss factor and relative dielectric constant among others. The increase in 0.5 phr volume resistivity with loading of nanofillers reported.