To provide a hydrocracking catalyst composition for hydrocarbon oil which shows high cracking activity and exerts excellent effects, e.g. a high yield of the middle fraction, when employed in hydrocracking of a heavy hydrocarbon oil, e.g. deasphaltene oil.

The composition consists of a hydrogenating metal component carried in a support comprising an aluminum-reinserted type Y zeolite having properties of (a) a unit lattice constant of 24.25-24.60 , (b) a degree of crystallinity of ≥95%, (c) a specific surface area of ≥500 m2/g, (d) a total pore volume of the group of micro pores of a 600 or smaller diameter of 0.45-0.70 ml/g, (e) a total pore volume of the group of micro pores of a 100--600 diameter of 0.10-0.40 ml/g, (f) a total pore volume of the group of micro pores of a 35-50 diameter of 0.03-0.15 ml/g and (g) a ratio of tetra-coordinated aluminum atoms to all the aluminum atoms in the zeolite of ≥60 atom% and a porous inorganic oxide.