A process for producing a gasoline base, the process comprising: a first step of hydrodesulfurizing of catalytically-cracked gasoline so as to result in an olefin hydrogenation rate of no greater than 25 mol% in the catalytically-cracked gasoline, a total sulfur content of no greater than 20 ppm by weight based on the product oil weight, a sulfur content derived from thiophenes and benzothiophenes of no greater than 5 ppm by weight and a sulfur content derived from thiacyclopentanes of no greater than 0.1 ppm by weight, and a second step of further hydrodesulfurizing of the product oil obtained by the first step so as to result in a total of no greater than 30 mol% for the olefin hydrogenation rate in the first step and the olefin hydrogenation rate in the second step, a total sulfur content of no greater than 10 ppm by weight based on the product oil weight, and a sulfur content derived from thiols of no greater than 5 ppm by weight, wherein the catalytically-cracked gasoline supplied for the first step is a heavy fraction from which the light fraction has been separated by distillation, with a boiling point range of 80-210°C, and a total sulfur content of no greater than 1000 ppm by weight based on the catalytically-cracked gasoline weight, wherein the catalyst used in the second step of the invention is a catalyst comprising one or more metals selected from among cobalt, molybdenum, nickel and tungsten, wherein the catalyst used in the first step is a catalyst obtained by loading one or more metals selected from among cobalt, molybdenum, nickel and tungsten on a support comprising a metal oxide composed mainly of alumina and containing at least one metal component selected from the group consisting of alumina-modifying alkali metals, iron, chromium, cobalt, nickel, copper, zinc, yttrium, scandium and lanthanoid metals, and wherein the reaction conditions in the first step are a reaction temperature of 200-270°C, a reaction pressure of 1-3 MPa, an LHSV of 2-7 h -1 and a hydrogen/oil ratio of 100-600 NL/L, and the reaction conditions in the second step are a reaction temperature of 300-350°C, a reaction pressure of 1-3 MPa, an LHSV of 10-30 h -1 and a hydrogen/oil ratio of 100-600 NL/L. a first step of hydrodesulfurizing of catalytically-cracked gasoline so as to result in an olefin hydrogenation rate of no greater than 25 mol% in the catalytically-cracked gasoline, a total sulfur content of no greater than 20 ppm by weight based on the product oil weight, a sulfur content derived from thiophenes and benzothiophenes of no greater than 5 ppm by weight and a sulfur content derived from thiacyclopentanes of no greater than 0.1 ppm by weight, and a second step of further hydrodesulfurizing of the product oil obtained by the first step so as to result in a total of no greater than 30 mol% for the olefin hydrogenation rate in the first step and the olefin hydrogenation rate in the second step, a total sulfur content of no greater than 10 ppm by weight based on the product oil weight, and a sulfur content derived from thiols of no greater than 5 ppm by weight, wherein the catalytically-cracked gasoline supplied for the first step is a heavy fraction from which the light fraction has been separated by distillation, with a boiling point range of 80-210°C, and a total sulfur content of no greater than 1000 ppm by weight based on the catalytically-cracked gasoline weight, wherein the catalyst used in the second step of the invention is a catalyst comprising one or more metals selected from among cobalt, molybdenum, nickel and tungsten, wherein the catalyst used in the first step is a catalyst obtained by loading one or more metals selected from among cobalt, molybdenum, nickel and tungsten on a support comprising a metal oxide composed mainly of alumina and containing at least one metal component selected from the group consisting of alumina-modifying alkali metals, iron, chromium, cobalt, nickel, copper, zinc, yttrium, scandium and lanthanoid metals, and wherein the reaction conditions in the first step are a reaction temperature of 200-270°C, a reaction pressure of 1-3 MPa, an LHSV of 2-7 h -1 and a hydrogen/oil ratio of 100-600 NL/L, and the reaction conditions in the second step are a reaction temperature of 300-350°C, a reaction pressure of 1-3 MPa, an LHSV of 10-30 h -1 and a hydrogen/oil ratio of 100-600 NL/L.