A process for adsorbing hydrocarbons from an acid gas stream includes passing the acid gas stream through an adsorbent which selectively removes hydrocarbons, desorbing the hydrocarbons from the adsorbent and contacting the desorbed hydrocarbons with an acid gas removal solution to remove acid gases which have been coadsorbed with the hydrocarbons. The process is particularly useful in removing hydrocarbons from a hydrogen sulfide-containing stream which is being directed to Claus processing for conversion into elemental sulfur. Useful adsorbents include crystalline titanium silicate molecular sieves containing titania octahedral sites such as ETS-10 and similar materials, as well as high silica aluminosilicate zeolite.