In this study, ethylene-propylene-diene monomer (EPDM) composites reinforced with graphene nanoplatelets (GnPs) and carbon black (CB) fillers and their hybrid combinations of various contents were prepared and examined. The size effect (lateral size and specific surface area) of GnPs and filler hybridization effects between GnPs and CB on the electrical and thermal conductivity of the EPDM composites were examined. The lateral size of GnPs is a more decisive factor in the thermal conductivity of composites than their specific specific surface area, and GnPs with a higher lateral size give better thermal conductivity. The addition of GnPs with a high lateral size and low specific specific surface area results in an almost one-fold increase in thermal conductivity. After a certain filler concentration, a synergistic effect of GnPs and CB on the thermal conductivity can be observed. Up to 20 phr GnPs, the specific surface area or lateral size of GnPs has a slight effect on the electrical conductivity of EPDM/GnPs composites. Higher electrical conductivity was achieved when hybrid fillers, 50 phr CB and 7 phr GnPs with higher lateral size were used for composite preparation. The morphology of the composite samples and the dispersion of all used fillers and hybrids were examined using transmission electron microscopy (TEM) and scanning electron microscopy (SEM).