The invention discloses a natural gas engine fuel supply method and system. The natural gas engine fuel supply method comprises the steps that S10, evaporation gas of liquified natural gas is pressurized to the natural gas critical pressure; S20, the evaporation gas is cooled to the natural gas critical temperature; S30, the evaporation gas is pressurized to the gas inlet pressure of a natural gasengine; S40, the evaporation gas is heated to the gas inlet temperature of the natural gas engine; and S50, the evaporation gas is led into the natural gas engine, and the steps are performed in sequence. The natural gas engine fuel supply system comprises a low-pressure compressor, a cooler, a high-pressure compressor and a heat exchanger, wherein the high-pressure compressor is driven by a drive device. The natural gas engine fuel supply method is simple in technological process, easy to operate and low in compression consumed power; and the supply system is simple, compact, small in size,small in occupied space, and capable of being used for effectively saving internal space of an LNG ship.