Understanding the mechanisms that govern the conductive properties of multifunctional cement-materials is fundamental for the development of the new applications proposed to enhance the energy efficiency, safety and structural properties of smart buildings and infrastructures. Many fillers have been suggested to increase the electrical conduction in concretes; however, the processes involved are still not entirely known. In the present work, we investigated the effect of graphene nanoplatelets (1 wt% on the electrical properties of cement composites (OPC/GNPs). We found a decrease of the bulk resistivity in the composite associated to the enhancement of the charge transport properties in the sample. Moreover, the study of the dielectric properties suggests that the main contribution to conduction is given by water diffusion through the porous network resulting in ion conductivity. Finally, the results support that the increase of direct current in OPC/GNPs is due to pore refinement induced by graphene nanoplatelets.