Batteries including lithium-ion, lead-acid, redox-flow and liquid-metal batteries show promise for grid-scale storage, but they are still far from meeting the grid's storage needs such as low cost, long cycle life, reliable safety and reasonable energy density for cost and footprint reduction. Here, we report a rechargeable manganese-hydrogen battery, where the cathode is cycled between soluble Mn2+ and solid MnO2 with a two-electron reaction, and the anode is cycled between H2 gas and H2O through well-known catalytic reactions of hydrogen evolution and oxidation. This battery chemistry exhibits a discharge voltage of 1.3 V, a rate capability of 100 mA cm-2 (36 s of discharge) and a lifetime of more than 10,000 cycles without decay. We achieve a gravimetric energy density of 139 Wh kg-1 (volumetric energy density of 210 Wh l-1), with the theoretical gravimetric energy density of 174 Wh kg-1 (volumetric energy density of 263 Wh l-1) in a 4 M MnSO4 electrolyte. The manganese-hydrogen battery involves low-cost abundant materials and has the potential to be scaled up for large-scale energy storage.