NOVELTY - A hydrogen generator (101) consists of a hydrodesulfurization device (51), a modifier (52), and a hydrogen-containing-gas flow path (54). The hydrodesulfurization device consists of catalyst layer (11) which converts sulfur compound contained in source gas into hydrogen sulfide, and catalyst layer (12) which adsorbs hydrogen sulfide. The modifier produces hydrogen-containing gas by reforming reaction using the source gas. The hydrogen-containing gas flowing through the flow path is heated sequentially by catalyst layers (11,12).    USE - Hydrogen generator is used in fuel-cell systems (claimed).    ADVANTAGE - The hydrogen generator is compact and has a simple structure. The hydrodesulfurization device is maintained at an appropriate temperature. The heat-use property of potential heat of the modifier is improved.    DETAILED DESCRIPTION - A hydrogen generator consists of a hydrodesulfurization device, a modifier, and a hydrogen-containing-gas flow path arranged to be adjoined with the modifier through a partition, through which hydrogen-containing gas sent from the modifier flows. The hydrodesulfurization device consists of catalyst layer (11) which converts sulfur compound contained in source gas into hydrogen sulfide, and catalyst layer (12) which adsorbs hydrogen sulfide. The modifier produces hydrogen-containing gas by reforming reaction using the source gas passing through the hydrodesulfurization device. The hydrogen-containing gas flowing through the flow path is heated sequentially by catalyst layers (11,12). An INDEPENDENT CLAIM is included for fuel-cell system provided with the hydrogen generator, and a fuel cell (100) which uses hydrogen-containing gas supplied from the hydrogen generator.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic block diagram of the hydrogen generator. (Drawing includes non-English language text)    Catalyst layers (11,12)    Hydrodesulfurization device (51)    Modifier (52)    Hydrogen-containing-gas flow path (54)    Mixed-gas flow path (56)    Fuel cell (100)    Hydrogen generator (101)