Graphene nanoplatelets (GNPs) employed as conductive fillers were added to an epoxy matrix, diglycidylether of bisphenol-A (DGEBA), to enhance the electrical conductivity and electromagnetic shielding efficiency of DGEBA. In addition, we investigated the influence of GNP fraction on the thermal properties, flexural strength, impact strength, electrical conductivity, electromagnetic shielding efficiency, and morphology of DGEBA/GNP nanocomposites. The electrical properties indicated that the electrical conductivity of DGEBA/GNP nanocomposites consisting of higher than 7.5 wt% GNPs was significantly improved compared to that of pristine DGEBA. The electromagnetic shielding efficiency of the nanocomposite showed a maximum value of 3.87 dB at 10 wt% GNPs, which is 287% higher than that of pristine DGEBA. An analysis of the fracture surfaces of the nanocomposites showed a rough morphology with numerous micro-cracks. In addition, the GNPs in the DGEBA matrix were stacked and formed a continuous conductive path at high GNP contents.