Organic sulfur compounds contained in refinery off gas streams having either high or low concentrations of olefins are converted to hydrogen sulfides which can be then be removed using conventional amine treating systems. The process uses a catalytic reactor with or without a hydrotreater depending on the olefin concentration of the off gas stream. The catalytic reactor operates in a hydrogenation mode or an oxidation mode to convert a majority of organic sulfur compounds into hydrogen sulfides.