We have successfully synthesized a new rhenium-based hexagonal bronze material, HgxReO3, which exhibits superconductivity with the transition temperature Tc=7.7 K at ambient pressure and 11.1 K at 4 GPa. This compound is a superconductor with the highest Tc among hexagonal bronzes. Moreover, it presents the novel crystallographic feature that (Hg2)2+ polycations, in contrast to monatomic cations in known hexagonal bronzes, are incorporated into open channels. There is evidence that conducting electrons tightly couple with Hg-related phonons. Our results inspire detailed studies on the role of the rattling phonon in the occurrence of superconductivity in the hexagonal bronzes.