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 hydrodesulfurization reaction stage. The hydrodesulfurized effluent stream is separated into a light and heavy liquid fraction and the heavier fraction is further processed in a mercaptan destruction reaction stage to reduce the content of mercaptan sulfur in the final product.