The invention relates to 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 (P), silicon (Si), boron (B), nickel (Ni) and cobalt (Co), the said element being taken alone, M is one or more element(s) selected from molybdenum (Mo), tungsten (W), nickel (Ni) and cobalt (Co), O is oxygen, H is hydrogen, h is an integer within the range 0 to 12, x is an integer within the range 0 to 4, m is an integer equal to 5, 6, 7, 8, 9, 10, 11, 12 and 18, y is an integer within the range 17 to 72 and q is an integer within the range 1 to 20, the said polyoxometalates being present within a mesostructured silicon oxide matrix having a pore size within the range 1.5 to 50 nm and having amorphous walls of thickness within the range 1 to 30 nm, the said catalyst being sulphured before being implemented in the said process.