A process and system for treating a hydroprocessing unit effluent gas stream for recycling includes introducing the effluent gas stream into a hydrogen purification zone and recovering a hydrogen-rich gas stream and a liquid stream containing a mixture that includes C1 to C4 hydrocarbons and H2S which is then mixed with an oxidant and fed to an oxidation unit containing catalyst for conversion of the H2S to elemental sulfur vapors that is separated for recovery of the elemental sulfur, and recovering a sweetened mixture that includes C1 to C4 hydrocarbons. Alternatively, the hydroprocessing unit effluent gas stream containing H2S is cooled, contacted with a solvent to absorb the C1 to C4 hydrocarbons and H2S, with the hydrogen-rich stream being recovered for recycling to the hydroprocessing unit, and the rich liquid solvent being flashed to produce a lean solvent stream for recycling to the adsorption zone and a mixed gas stream that includes the C1 to C4 hydrocarbons and H2S that is passed to an oxidation zone and is reacted with an oxidant in the presence of a catalyst to complete the process as described above for the recovery of elemental sulfur and a mixture that includes the sweetened C1 to C4 hydrocarbons.