The invention concerns a process for converting heavy feeds carried out in a slurry reactor in the presence of hydrogen and in the presence of a catalyst comprising at least one catalytic metal or a compound of a catalytic metal from group VIB and/or VIII supported on alumina, the pore structure of which is composed of a plurality of juxtaposed agglomerates each formed by a plurality of acicular platelets, the platelets of each agglomerate being generally radially oriented with respect to the others and with respect to the centre of the agglomerate, said catalyst having an irregular and non-spherical shape and being mainly in the form of fragments, obtained using a process including the following steps: a) granulation starting from an active alumina powder having a low crystallinity and/or amorphous structure, to obtain agglomerates in the form of beads; b) maturing in a moist atmosphere between 60° C. and 100° C. then drying said beads; c) sieving to recover a fraction of said beads; d) crushing said fraction; e) calcining at least a portion of said crushed fraction at a temperature in the range 250° C. to 900° C.; f) impregnating with acid and hydrothermal treatment at a temperature in the range 80° C. to 250° C.; g) drying then calcining at a temperature in the range 500° C. to 1100° C. h) depositing at least one catalytic metal or compound of a catalytic metal from group VIB and/or group VIII by impregnation. The process of the invention employs a catalyst with a specific pore texture, shape and granulometry, resulting in improved performances.