NOVELTY - A liquid fuel desulfurization system comprises desulfurizer where pre-heated undesulfurized liquid fuel flows in and which removes sulfur content by desulfurization catalyst, heat retention unit which heat retains undesulfurized liquid fuel, desulfurization fuel feed pump (4) which supplies desulfurization liquid fuel to modifier, safety valve or relief valve which opens when pressure in desulfurizer exceeds limit value, and by pass valve which closes when predetermined time progress.    USE - A liquid fuel desulfurization system for polymer electrolyte fuel cell system.    ADVANTAGE - The liquid fuel desulfurization system can safely supply liquid fuel to a modifier.    DETAILED DESCRIPTION - A liquid fuel desulfurization system comprises undesulfurized fuel tank where undesulfurized liquid fuel is accommodated, pump which pressure rises under sulfurized liquid fuel, preheater (5) which pre-heats undesulfurized liquid fuel, desulfurizer where pre-heated undesulfurized liquid fuel flows in and which removes sulfur content by desulfurization catalyst, heat retention unit which heat retains undesulfurized liquid fuel, desulfurization fuel tank which holds desulfurization liquid fuel that flows in through pressure control valve (7) and desulfurization fuel supply valve, desulfurization fuel feed pump (4) which supplies desulfurization liquid fuel to modifier, safety valve or relief valve which opens when pressure in desulfurizer exceeds limit value, and by pass valve which closes when predetermined time progress. The desulfurization fuel tank is connected to anode waste gas piping which leads to combustor (13) of modifier through non-return valve. An INDEPENDENT CLAIM is included for a method of operating liquid fuel desulfurization system.    DESCRIPTION OF DRAWING(S) - The drawing shows a system block diagram of the liquid fuel desulfurization system. (Drawing includes non-English language text).    Desulfurization fuel feed pump (4)    Liquid fuel preheater (5)    Pressure control valve (7)    Combustor (13)    Pressure sensor (17)