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 center of the agglomerate, the catalyst having an irregular and nonspherical shape and being mainly in the form of fragments. The process of the invention employs a catalyst with a specific pore texture, shape and granulometry, resulting in improved performances.