TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Adsorbent : The adsorbent has a specific area of 20 m2/g or more (preferably 50 m2/g or more). The primary particles of the cerium oxide have a mean crystalline diameter of 10 nm or less. The adsorbent contains cerium oxide having a hydrogen consumption at 600 degreesC or lower in a temperature-increasing reduction test of 200 mumol/g or more (preferably 300 mumol or more). In the adsorbent, at least one element selected from groups 1 - 15 in the periodic table is carried on the cerium oxide.Preferred Process : The adsorbent is obtained by baking cerium oxide carrying 1 - 90 wt% based on the total wt of the adsorbent of at least one element selected from groups 1 - 15 in the periodic table at 400 degreesC or lower. The cerium oxide is a composite oxide containing at least one metal element selected from groups 2 - 16 in the periodic table. The hydrocarbon fuel is at least one hydrocarbon selected from LPG, city gas, natural gas, naphtha, paraffin oil, light oil, ethane, ethylene, propane, butane, butene, methanol and dimethyl ether or a hydrocarbon containing an oxygen atom. The process for producing H2 comprises removing sulfur compounds from hydrocarbon fuel using the invented adsorbent and bringing the resulting hydrocarbon fuel into contact with a partially oxidized quality-improving catalyst, an autothermal quality-improving catalyst or a steam quality-improving catalyst, which is an Ru- or Ni-catalyst. The sulfur compound-removal treatment is carried out without adding H2 or O2. The sulfur compound is at least one compound selected from SCO, CS2, H2S, mercaptans, sulfides and thiophenes. The sulfur compound-removal treatment is carried out at 200 degreesC or lower (preferably 100 degreesC or lower). WIDER DISCLOSURE - A process for producing H2 comprises removing sulfur compounds from a hydrocarbon fuel using the invented adsorbent. A fuel cell system utilizes the H2 obtained by the invented process.    EXAMPLE - CeNO3.6H2O (470 g) was dissolved in ion-exchanged water (1 liter) at 50 degreesC. The obtained solution and a 3 mol/liter NaOH aqueous solution were mixed so as to obtain a solution having a pH of 13. The solution was stirred at 50 degreesC for 1 hour. The generated solid was filtered, washed with ion-exchanged water (2 liter), dried by flowing hot air (at 110 degreesC) for 12 hours and baked at 350 degreesC for 3 hours. The product was pulverized and molded into tablets so as to obtain an adsorbent having a specific area of 147 m2/g and a mean crystal diameter of 5 nm. Propane gas containing 10 vol ppm of COS, 10 vol ppm of dimethylsulfide, 10 vol ppm of t-butylmercaptan and 10 vol ppm of dimethylsulfide, was passed at a GHSV of 30,000 h-1 through a tube (i.d. = 9 mm) filled with the adsorbent (1 cm3) at 20 degreesC. The adsorbent adsorbed 1.42 g/ml of S, and it has a life time of 5 hours.