In the present study, we develop a conductive copper/carbon nanomaterial additive and investigate the effects of the morphologies of the carbon nanomaterials on the conductivities of composites containing the additive. The conductive additive is prepared by mechanically milling copper powder with carbon nanomaterials, namely, multi-walled carbon nanotubes (MWCNTs) and/or few-layer graphene (FLG). During the milling process, the carbon nanomaterials are partially embedded in the surfaces of the copper powder, such that electrically conductive pathways are formed when the powder is used in an epoxy-based composite. The conductivities of the composites increase with the volume of the carbon nanomaterial. For a constant volume of carbon nanomaterial, the FLG is observed to provide more conducting pathways than the MWCNTs, although the optimum conductivity is obtained when a mixture of FLG and MWCNTs is used.