The electrical conductivities, dielectric properties and electromagnetic shielding efficiency of graphene oxide (GO)/epoxy nanocomposites are studied. Composites containing self-aligned reduced GO (rGO) sheets are fabricated using an all aqueous method. The aligned graphene nanocomposites display significant anisotropy in properties measured in the directions of alignment and perpendicular to it. The rGO/epoxy nanocomposites present a very low percolation threshold of 0.26 wt% as a result of fine dispersion of monolayer rGO sheets and their ultralarge size. The composites exhibit exceptionally high dielectric constants depending on the graphene content due to the charge accumulation at the highly conductive filler/insulating polymer interface according to the polarization principle. The highly dielectric nanocomposites can function as effective electromagnetic interference (EMI) shielding materials.