An LNG BOG(Liquefied Natural Gas Boil-Off Gas) reliquefaction apparatus and a method are provided to reduce the power consumption by compressing nitrogen at low pressure by lowering the temperature of BOG supplied to a condenser. An LNG BOG reliquefaction apparatus is composed of a BOG cycle for compressing BOG generated in an LNG storage tank by a BOG compression unit(110) and then condensing the BOG by a condensing unit and a nitrogen cycle for supplying cold heat to the condensing unit. The nitrogen cycle comprises a nitrogen gas compression unit(130) and an expansion unit expanding the compressed nitrogen gas. A unit for recovering cold heat of the BOG discharged from the storage tank by heat-exchanging the BOG discharged from the storage tank and high-temperature fluid is installed at a BOG line formed between the storage tank and the BOG compression unit. A nitrogen gas separating unit(200) for reducing the content of nitrogen in the BOG by separating and removing some of the nitrogen gas in the compressed BOG and delivering methane of high concentration to the BOG again is installed between the BOG compression unit and the nitrogen cycle. The expansion unit comprises an expansion valve and an expansion turbine(134) receiving the compressed nitrogen gas branched off.
