The invention relates to a process for the hydrodesulfurization of a sulfur-containing olefinic gasoline cut in which said gasoline cut, hydrogen and a regenerated catalyst are brought into contact, said process being carried out at a temperature of between 200° C. and 400° C., a total pressure of between 1 and 3 MPa, an hourly space velocity, defined as being the flow rate by volume of feedstock relative to the volume of catalyst, of between 1 and 10 h−1; and a hydrogen/gasoline feedstock ratio by volume of between 100 and 1200 SI/I, said regenerated catalyst resulting from an at least partially spent catalyst resulting from a process for the hydrodesulfurization of a sulfur-containing olefinic gasoline cut and comprises at least one metal from group VIII, at least one metal from group VIb and an oxide support.