An apparatus for supplying a liquid fuel gas comprising - a distillation tower into which a liquefied natural gas is guided as a source material, whereafter a methane-rich natural gas is prepared from a gas component guided out from a tower top portion of the distillation tower, and a natural gas liquid is prepared from a liquid component guided out from a tower bottom portion of the distillation tower, having: - a source material supplying flow passageway in which the pressurized liquefied natural gas in a supercooled state is guided as the source material into the distillation tower via a source material supplying portion, a first heat exchanger, a second heat exchanger, a third heat exchanger, a vaporizer, an expander, the second heat exchanger again, and a gas-liquid separator; - a methane-rich natural gas supplying flow passageway in which one gas component A derived from branching of the gas component is supplied out as the methane-rich natural gas via a compressor linked to the expander and a methane-rich natural gas supplying portion; - a reflux flow passageway in which the other gas component B derived from branching of the gas component is guided as a reflux liquid into an upper portion of the distillation tower via the first heat exchanger; and - a natural gas liquid supplying flow passageway in which the liquid component is supplied out as the natural gas liquid via the third heat exchanger and a natural gas liquid supplying portion, wherein • in the first heat exchanger, the gas component B is subjected to condensation by coldness of the liquefied natural gas supplied from the source material supplying portion, thereby to prepare the reflux liquid, • in the second heat exchanger, the expanded natural gas guided out from the expander is subjected to low-temperature condensation by coldness of the liquefied natural gas guided out from the first heat exchanger, thereby to prepare the source material, and • in the third heat exchanger, the liquid component guided out from the tower bottom portion is subjected to lowering of temperature by coldness of the liquefied natural gas guided out from the second heat exchanger, thereby to prepare the natural gas liquid. - a distillation tower into which a liquefied natural gas is guided as a source material, whereafter a methane-rich natural gas is prepared from a gas component guided out from a tower top portion of the distillation tower, and a natural gas liquid is prepared from a liquid component guided out from a tower bottom portion of the distillation tower, having: - a source material supplying flow passageway in which the pressurized liquefied natural gas in a supercooled state is guided as the source material into the distillation tower via a source material supplying portion, a first heat exchanger, a second heat exchanger, a third heat exchanger, a vaporizer, an expander, the second heat exchanger again, and a gas-liquid separator; - a methane-rich natural gas supplying flow passageway in which one gas component A derived from branching of the gas component is supplied out as the methane-rich natural gas via a compressor linked to the expander and a methane-rich natural gas supplying portion; - a reflux flow passageway in which the other gas component B derived from branching of the gas component is guided as a reflux liquid into an upper portion of the distillation tower via the first heat exchanger; and - a natural gas liquid supplying flow passageway in which the liquid component is supplied out as the natural gas liquid via the third heat exchanger and a natural gas liquid supplying portion, wherein • in the first heat exchanger, the gas component B is subjected to condensation by coldness of the liquefied natural gas supplied from the source material supplying portion, thereby to prepare the reflux liquid, • in the second heat exchanger, the expanded natural gas guided out from the expander is subjected to low-temperature condensation by coldness of the liquefied natural gas guided out from the first heat exchanger, thereby to prepare the source material, and • in the third heat exchanger, the liquid component guided out from the tower bottom portion is subjected to lowering of temperature by coldness of the liquefied natural gas guided out from the second heat exchanger, thereby to prepare the natural gas liquid. • in the first heat exchanger, the gas component B is subjected to condensation by coldness of the liquefied natural gas supplied from the source material supplying portion, thereby to prepare the reflux liquid, • in the second heat exchanger, the expanded natural gas guided out from the expander is subjected to low-temperature condensation by coldness of the liquefied natural gas guided out from the first heat exchanger, thereby to prepare the source material, and • in the third heat exchanger, the liquid component guided out from the tower bottom portion is subjected to lowering of temperature by coldness of the liquefied natural gas guided out from the second heat exchanger, thereby to prepare the natural gas liquid.