In this paper, we report how few layers graphene that can be produced in large quantity with low defect ratio from exfoliation of graphite by using a high intensity probe sonication in water containing liquid hand soap and PVP. It was founded that the graphene powder obtained by this simple exfoliation method after the heat treatment had an excellent exfoliation into a single or layered graphene sheets. The UV-visible spectroscopy, FESEM, TEM, X-ray powder diffraction and Raman spectroscopy was used to analyse the graphene product. The thermal diffusivity of the samples was analysed using a highly accurate thermal-wave cavity photothermal technique. The data obtained showed excellent enhancement in the thermal diffusivity of the graphene dispersion. This well-dispersed graphene was then used to fabricate an electrically conductive polymer-graphene film composite. The results demonstrated that this low cost and environmental friendly technique allowed to the production of high quality layered graphene sheets, improved the thermal and electrical properties. This may find use in the wide range of applications based on graphene.