  Finding intrinsic carbon superconductor is an interesting topic. Based on
density functional first-principles calculations, we first study the
phonon-mediated superconductivity in a cubic metallic carbon allotrope, namely
sc-C$_{20}$, which has been synthesized in experiment. The electron-phonon
coupling is accurately computed with Wannier interpolation method. By solving
the Eliashberg equations, we predict that sc-C$_{20}$ is an intrinsic carbon
superconductor, without introducing any guest atoms or doping, whose transition
temperature is determined to be about 24 K. Our findings enrich the family of
carbon-based superconductors.
