Hydrogen sulfide is removed from a fluid stream by contacting the fluid stream which contains hydrogen sulfide with an absorbing composition comprising zinc, titanium and at least one promoter selected from the group consisting of vanadium, chromium, manganese, iron, cobalt, nickel, molybdenum, rhenium, and compounds thereof. If organic sulfur compounds are present in the fluid stream, the absorbing composition acts as a hydrodesulfurization catalyst to convert the sulfur in the organic sulfur compounds to hydrogen sulfide which is subsequently removed from the fluid stream by the absorbing composition. If olefin contaminants are present in the fluid stream, the absorbing composition acts as hydrogenation catalyst to hydrogenate the olefin contaminants to paraffins.