A process for the hydrocracking a hydrocarbon-containing feedstock in which at least 50% by weight of the compounds have an initial boiling point above 340° C. and a final boiling point below 540° C., using a catalyst having, in its oxide form, at least one metal selected from the metals of groups VIB, VIII and VB, said metals being present in the form of at least one polyoxometallate of formula (HhXxMmOy)q−, said polyoxometallates being present within a mesostructured matrix based on oxide of at least one element Y, said matrix having a pore size between 1.5 and 50 nm and having amorphous walls of thickness between 1 and 30 nm, said catalyst being sulphurized before used in said process.