The present application concerns a process for the treatment of a gasoline containing sulphur-containing compounds and olefins, with the following steps: a) a step for hydrodesulphurization of said gasoline in order to produce an effluent which is depleted in sulphur by passing the gasoline mixed with hydrogen over at least one hydrodesulphurization catalyst; b) a step for separating the partially desulphurized gasoline from the hydrogen introduced in excess as well as the H2S formed during step a); c) a catalytic step for sweetening desulphurized gasoline obtained from step b), which converts residual mercaptans into thioethers via an addition reaction with the olefins.