In a process for granulating slag, from a blast furnace or a smelting reduction plant, in which a granule/water mixture formed during the granulation is fed to a granulation tank and then to a dewatering installation, in which the slag granules are dewatered. H.sub.2S-containing vapors and gases formed during the granulation are at least partially condensed by injection of water in a condensation space which is flow-connected to the granulation tank. H.sub.2S-containing residual gases are discharged from the compensation space below the water injection point, H.sub.2S is burnt.