A method for hydrocracking a heavy fraction oil which comprises cracking a heavy fraction oil in the coexistence of a catalyst and a hydrogen donating solvent such as tetralin while adding a hydrogen-containing gas to the cracking reactor thereby inhibiting the formation of carbonaceous substances and precursors thereof and then hydrogenating the reaction products in the presence of a solid catalyst while adding a hydrogen-containing gas to the hydrogenating reactor thereby to convert the toluene-insoluble carbonaceous substances and precursors thereof to toluene-soluble ones, thus causing no clogging in an apparatus used.
