Improving kinetics of solid-state sulfide conversion in sulfur cathodes can enhance sulfur utilization of metal-sulfur batteries. However, fundamental understanding of the solid-state conversion remains to be achieved. Here, taking potassium-sulfur batteries as a model system, we for the first time report the reducing overpotential of solid-state sulfide conversion via the meta-stable S32- intermediates on transition metal single-atom sulfur hosts. The catalytic sulfur host containing Cu single atoms demonstrates high capacities of 1595 and 1226 mAh g-1 at current densities of 335 and 1675 mA g-1 , respectively, with stable Coulombic efficiency of ≈100 %. Combined spectroscopic characterizations and theoretical computations reveal that the relatively weak Cu-S bonding results in low overpotential of solid-state sulfide conversion and high sulfur utilization. The elucidation of solid-state sulfide conversion mechanism can direct the exploration of highly efficient metal-sulfur batteries.