A process for the selective hydrogenation of a gasoline comprising polyunsaturated compounds and light sulfur compounds, process wherein the gasoline and hydrogen are brought into contact with a catalyst, at a temperature between 80° C. and 220° C., with a liquid space velocity of between 1 h−1 and 10 h−1 and a pressure of between 0.5 and 5 MPa, and with a molar ratio between hydrogen and the diolefins to be hydrogenated of greater than 1 and less than 100 mol/mol, said catalyst comprising at least one group VIB metal, at least one group VIII metal, and a mesoporous and macroporous alumina support comprising a bimodal distribution of mesopores and wherein:
- the volume of mesopores with a diameter greater than or equal to 2 nm and less than 18 nm corresponds to between 10% and 30% by volume of the total pore volume of said support;
- the volume of mesopores with a diameter greater than or equal to 18 nm and less than 50 nm corresponds to between 30% and 50% by volume of the total pore volume of said support;
- the volume of macropores with a diameter greater than or equal to 50 nm and less than 8000 nm corresponds to between 30% and 50% by volume of the total pore volume of said support.