The invention concerns a process for desulphurizing gasoline comprising a step for fractionating said gasoline under conditions in which a light fraction comprising the lightest thiophene compounds such as thiophene or methylthiophenes and a heavy fraction concentrating the heaviest aromatic sulphur-containing compounds are obtained. Said heavy fraction is treated by hydrodesulphurization, while the light fraction is brought into contact with a solid adsorbant to eliminate at least a portion of said light thiophene compounds.