The invention provides a method and a device applied to constant-pressure recovery of liquefied natural gas flash steam. The method comprises the following steps: feeding supercooled and liquefied natural gas by a low-temperature storage tank and introducing the supercooled and liquefied natural gas into a low-temperature pressure container to arrive at a filler bed; boosting the liquefied natural gas flash steam generated in the low-temperature storage tank by a low-temperature compressor and feeding the liquefied natural gas flash steam into the filler bed of the low-temperature pressure container; exchanging heat of the liquefied natural gas flash steam introduced into the low-temperature pressure container and the supercooled and liquefied natural gas by virtue of materials of the filler bed, and instantly dissolving the liquefied natural gas flash steam in supercooled and liquefied natural gas in the unsaturated state; feeding high-pressure nitrogen into the low-temperature pressure container to enable the pressure to be constant; converting all the liquefied natural gas flash steam from gaseous state into liquid state, and enabling all the liquefied natural gas in the process of dissolving the liquefied natural gas flash steam to flow out of the low-temperature pressure container and enter subsequent technical processes. The device comprises a low-temperature pressure container, wherein the low-temperature pressure container is internally provided with the filler bed. The device is stable in running, high in safety and low in emission; the vibration noise is reduced; the operation cost is lowered.