Fuel supply system for an internal combustion engine and a fuel supply method

The fuel supply system for an internal combustion engine comprises a heat exchanger (20), having a heat exchanger located in the liquefied fuel passage (20a) and the heat exchange between the engine coolant passage (20b) exchange wall. The fuel heated and vaporized liquefied fuel outflow passage from the heat exchanger is supplied to an internal combustion engine. Liquefied fuel flow rate supplied to the heat exchanger of the liquefied fuel passage is set. Flow rate of engine coolant is supplied to the engine coolant passages of the heat exchanger based on the temperature of the engine coolant supplied to a heat exchanger of an engine coolant passage is determined such that the set flow rate of the liquefied fuel under the nucleate boiling transition or boiling liquefied fuel passage in the vicinity of the boundary in the transition boiling and nucleate boiling occurs between.