A process for the selective hydrodesulfurization of olefinic naphtha streams containing a substantial amount of organically bound sulfur and olefins. The olefinic naphtha stream is selectively desulfurized in a first hydrodesulfurization reaction stage. This effluent stream is then contacted with a stripping agent in a H2S removal zone, such as steam or an amine solution, to remove H2S from the effluent stream, thereby reducing the H2S partial pressure of the process stream. The process stream is then subjected to a second desulfurization reaction stage followed by a mercaptan decomposition stage to reduce the content of mercaptan sulfur in the final product stream. In a second embodiment, the effluent stream from the first hydrodesulfurization reaction stage, after being subjected to the H2S removal zone, is fed directly to the mercaptan decomposition stage where total sulfur content and mercaptan sulfur content are reduced in the final product stream.