A method for the two-step catalytic hydrogenation treatment of a heavy hydrocarbon oil which comprisesfirst contacting the heavy hydrocarbon oil with a first solid catalyst comprising a metal component having catalytic activity for hydrogenation supported on a zeolite having catalytic activity for cracking a hydrocarbon, said zeolite having a (i) pore size distribution curve with two peaks, one peak in the range of 5 to 50 nm pore diameter and the other peak in the range of 50 to 1000 nm pore diameter and (ii) the volume of the pores having a diameter of 100 nm or larger is at least 0.05 ml/g; andthen contacting the heavy hydrocarbon oil which had been contacted with said first catalyst, with a second catalyst, said second catalyst having hydrogenation activity and which is different from said first catalyst.