A process of hydrodesulphuration of at least one gasoline cut implementing a catalyst comprising, in its oxide form, at least one metal from group VIB and/or at least one metal from group VIII of the periodic table, present in the form of at least one polyoxometalate of the formula (HhXxMmOy)q−, wherein X is an element selected from phosphorus, silicon, boron, nickel and cobalt, M is one or more element(s) selected from molybdenum, tungsten, nickel and cobalt, h is an integer from 0-12, x is an integer from 0-4, m is an integer 5, 6, 7, 8, 9, 10, 11, 12 and/or 18, y is an integer of 17-72 and q is an integer of 1-20, the polyoxometalates being present within a mesostructured silicon oxide matrix having a pore size of 1.5-50 nm and having amorphous walls of thickness 1-30 nm, the catalyst being sulphured before use in the process.