In order to increase the thermal conductivity of neat epoxy resin and broaden its practical application in high-voltage insulation systems, we have constructed four kinds of epoxy resin nanocomposite models (a neat epoxy resin (EP), a graphene-doped epoxy resin nanocomposite (EP/GR) and hydroxyl- or carboxyl-functionalized graphene-doped epoxy resin nanocomposites (EP/GR-OH or EP/GR-COOH)) to systematically investigate their thermodynamic and electrical properties using molecular dynamics (MD) simulations. Compared with the EP model, carboxyl-functionalized graphene particles enhanced the thermal conductivity of the EP/GR-COOH model by 66.5% and increased its T_g by 26.6 K. Furthermore, the dielectric constant of the EP/GR-COOH model was significantly reduced. To investigate the intrinsic mechanism, the lowest fraction of free volume (13.22%) and the largest number of hydrogen bonds (102.2) in the EP/GR-COOH model were identified as playing essential roles for its excellent thermodynamic properties and favorable electrical performance. The present study provides a molecular-level understanding of the satisfactory thermodynamic and electrical properties of the EP/GR-COOH nanocomposite, which will aid in designing novel epoxy resin nanocomposite materials with high thermal conductivity.