The invention relates to a method of producing sulfuric acid wherein an SO.sub.2-containing raw gas produced in a sulfuric-acid recovery plant is passed through at least one reactor in which a catalytic reaction of SO.sub.2 to SO.sub.3 takes place, and the SO.sub.3 thereby formed is converted into sulfuric acid. According to the invention, at least a partial stream of the gas stream leaving the sulfuric-acid recovery plant is hydrogenated with an H.sub.2-rich gas in a post-treatment stage. The H.sub.2S-containing gas stream formed by the hydrogenation is fed into the H.sub.2S gas scrubber of a coke oven plant or a petrochemical plant. The invention also relates to an installation for carrying out the method.