A process for hydrodesulfurizing a sulfur-containing hydrocarbon which comprises contacting the sulfur-containing hydrocarbon under hydrodesulfurizing conditions in the presence of hydrogen with a catalyst composition comprising a Group VIA metal, a Group VIII metal and an alumina, the catalyst composition containing the Group VIA metal and the Group VIII metal in a combined amount of 20 to 70% by weight based on the total of the Group VIA metal, the Group VIII metal and the alumina. The catalyst composition being characterized by (i) an X-ray diffraction pattern having no diffraction peak other than that of the alumina, and, (ii) after being air-calcined at 550.degree. C. for three hours, being characterized by a TRP which results in a ratio of the area L of a low temperature reduction peak to the area H of a high temperature reduction peak, L/H, of 0.1 to 0.45.