Carbon has abundant allotropes with superhardness, but few of them are metallic. From first-principles calculations, we propose a stable metallic carbon allotrope (Hex-C24) phase with superhardness. The Hex-C24 can be thought of as a superlattice of carbon nanotubes and graphene nanoribbons composed of sp2- and sp3-hybridized carbon atoms. A possible synthetic route towards Hex-C24 from graphyne multilayers is evaluated by calculating the transition states between the two phases. Our calculations show that at a uniaxial pressure of around 25 GPa, the energy barrier of this endothermic transition is estimated to be 0.04 eV per atom, while at a pressure of 34 GPa, the transition is barrierless for specific initial configurations. The cohesive energy, elastic constants, and phonon frequencies unambiguously confirm the structural stability. The hardness of the Hex-C24 is estimated to exceed 44.54 GPa, which is 1/2 that of diamond. The Hex-C24 phase is metallic with several bands across the Fermi level. Both mechanical and metallic properties of Hex-C24 are anisotropic.