Disclosed herein is a process for efficiently and stably producing high-quality kerosene and gas oil from crude oil or crude oil from which naphtha fraction is removed through the hydrotreatment of the crude oil by using a specific hydrotreatment catalyst; a process capable of prolonging the service life of the catalyst; a process capable of extending the continuous operation period of the process equipment; a process simplifying a petroleum refinery equipment; and the like. There are used, as hydrotreatment catalysts in the hydrotreatment of a hydrocarbon oil, the metals each belonging to any of the groups 6, 8, 9 and 10 of the Periodic Table which metals are supported on a carrier composed of alumina/boria, metal-containing aluminosilicate, alumina/an alkaline earth metal compound, alumina/phosphorus, alumina/titania or alumina/zirconia.