The invention discloses a quickly driving system used in a floating liquid natural gas unit and a driving method thereof. The driving system comprises an LNG quick mixing precooling system, a precooling cryogen circulatory system, a deep cooling cryogen circulatory system and a storage system, wherein the LNG quick mixing precooling system is used for mixing LNG and natural gas and making the mixture enter a precooling heat exchanger; the precooling cryogen circulatory system is used for precooling virgin gas and deep cooling cryogen, a precooling circulation input end is connected to an outlet of an outlet cooler of a precooling cryogen compressor, and precooling cryogen returns to an inlet of the precooling cryogen compressor after being subjected to heat exchanging through the precooling heat exchanger; the deep cooling cryogen circulatory system is used for providing cooling capacity needed by liquefaction of raw natural gas, the input end of the deep cooling cryogen circulatory system is connected to an outlet of an outlet cooler of a deep cooling cryogen compressor and enters an inlet of the deep cooling cryogen compressor again after passing the precooling heat exchanger and a deep cooling heat exchanger, the virgin gas passes through the LNG quick mixing precooling system, the precooling heat exchanger and the deep cooling heat exchanger from a virgin gas pipeline to an LNG output pipeline; the storage system is used for introducing cooled LNG into an LNG storage tank to be subjected to storage and making the natural gas which is not liquefied burn at the same time.