A catalytic composition for hydrotreating of hydrocarbons in which a metallic component for hydrogenation is carried on a carrier comprising a porous inorganic oxide and aluminum- and titanium-inserted zeolite Y with aluminum and titanium inserted in a frame structure of the zeolite Y having been subjected to processing for removing aluminum, wherein the aluminum- and titanium-inserted zeolite Y used to prepare the catalytic composition has the following characteristics: (a) unit cell dimension in a range from 24.25 to 24.60 Å (b) crystallinity of 95 % or more, wherein the crystallinity is calculated through the following equation Crystallinity = H H 0 × 100 % where H is a total peak height on each of the,,,, and planes for X-ray diffraction of the zeolite Y, and H 0 is a peak height for each of the same planes for X-ray diffraction of zeolite Y SK-40, assuming that the crystallinity of the zeolite Y SK-40 is 100, (c) specific surface area of 500 m 2 /g or more, when measured by means of the BET method of nitrogen adsorption, (d) total pore volume (PVt) of a group of pores each having a diameter of 600 Å or below in a range from 0.45 to 0.70 ml/g, wherein the total pore volume (PVt) of pores each having a diameter in this range was obtained from a pore distribution obtained by calculating and analysing data for adsorptoin and desorption of nitrogen by means of the B.J.H. method, (e) pore volume (PVm) of a group of pores each having a diameter in a range from 100 to 600 Å in a range from 0.10 to 0.40 ml/g, (f) pore volume (PVs) of a group of pores each having a diameter in a range from 35 to 50 Å in a range from 0.03 to 0.15 ml/g, and (g) percentage of 4-coordinate aluminum atoms against total aluminum atoms in the zeolite of 60 atom % or more, wherein the percentage of 4-coordinate aluminum in the zeolite is obtained from the 27 Al MAS NMR spectrum measured by the nuclear magnetic resonance instrument VXR-400 produced by VARIAN Corp. (a) unit cell dimension in a range from 24.25 to 24.60 Å (b) crystallinity of 95 % or more, wherein the crystallinity is calculated through the following equation Crystallinity = H H 0 × 100 % where H is a total peak height on each of the,,,, and planes for X-ray diffraction of the zeolite Y, and H 0 is a peak height for each of the same planes for X-ray diffraction of zeolite Y SK-40, assuming that the crystallinity of the zeolite Y SK-40 is 100, (c) specific surface area of 500 m 2 /g or more, when measured by means of the BET method of nitrogen adsorption, (d) total pore volume (PVt) of a group of pores each having a diameter of 600 Å or below in a range from 0.45 to 0.70 ml/g, wherein the total pore volume (PVt) of pores each having a diameter in this range was obtained from a pore distribution obtained by calculating and analysing data for adsorptoin and desorption of nitrogen by means of the B.J.H. method, (e) pore volume (PVm) of a group of pores each having a diameter in a range from 100 to 600 Å in a range from 0.10 to 0.40 ml/g, (f) pore volume (PVs) of a group of pores each having a diameter in a range from 35 to 50 Å in a range from 0.03 to 0.15 ml/g, and (g) percentage of 4-coordinate aluminum atoms against total aluminum atoms in the zeolite of 60 atom % or more, wherein the percentage of 4-coordinate aluminum in the zeolite is obtained from the 27 Al MAS NMR spectrum measured by the nuclear magnetic resonance instrument VXR-400 produced by VARIAN Corp.