Provided is a method for producing liquefied natural gas by multi-component refrigerant two-stage compression. The method includes two multi-component refrigerant compression cycles, the refrigerant in a first cycle is called a pre-cooling refrigerant, the refrigerant in a second cycle is called a cryogenic refrigerant; the pre-cooling refrigerant returns to an ice chest after passing through a pre-cooling compressor, a cooler, a buffer tank, the ice chest, a throttle valve and a gas-liquid separation tank, and then returns to the pre-cooling compressor; the cryogenic refrigerant returns to the ice chest after passing through a cryogenic compressor, the cooler, the ice chest, the throttle valve and the gas-liquid separation tank, and then returns to the cryogenic compressor; and natural gas is cooled after heat transfer of the ice chest and the refrigerants and finally becomes the liquefied natural gas. The natural gas is liquefied by two independent multi-component refrigerant compression cycles, and composition and content of the two multi-component refrigerants are different, so that the method is wide in application range to raw material natural gas, high in operation flexibility and high in liquefying efficiency. Besides, the method is simple in liquefying process, low in investment cost, and is applicable to liquefied natural gas factories in various scales.