There is described a hydroprocessing process of at least one gas oil cut having a weighted mean temperature (TMP) between 240° C. and 350° C. using a catalyst comprising at least one metal of the group VIB and/or at least one metal of the group VIII of the periodic classification and a support comprising an amorphous mesoporous alumina having a connectivity (Z) greater than 2.7, the hydroprocessing process operating at a temperature between 250° C. and 400° C., at a total pressure between 2 MPa and 10 MPa with a ratio of hydrogen volume to volume of hydrocarbon-containing feedstock between 100 and 800 litres per litre and at an Hourly Volume Rate (HVR) which is defined by the ratio of the volume flow rate of liquid hydrocarbon-containing feedstock to volume of catalyst fed into the reactor between 1 and 10 h−1.