A process for selective hydrogenation of a gasoline comprising polyunsaturated compounds and light sulfur compounds having a boiling point lower than 84° C., said process comprising bringing into contact the gasoline and hydrogen with a catalyst, at a temperature of 80° C. to 220° C., with a liquid space velocity of 1 h−1 to 10 h−1 and a pressure of 0.5 to 5 MPa, and with a molar ratio between the hydrogen and diolefins to be hydrogenated in the gasoline 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 is 10% to 30% by volume of the total pore volume of said mesoporous and macroporous alumina support;
- the volume of mesopores with a diameter greater than or equal to 18 nm and less than 50 nm is 30% to 50% by volume of the total pore volume of said mesoporous and macroporous support;
- and
- the volume of macropores with a diameter greater than or equal to 50 nm and less than 8000 nm is 30% to 50% by volume of the total pore volume of said mesoporous and macroporous support.