A device and a method for producing hydrogen and byproduct oxygen by using green electricity electrolyzed water are provided. The device comprises an oxygen purifying system, a heat exchange system, an air separation compression and expansion system, an air separation rectification system and a liquid oxygen storage system. The method comprises the following steps: first, purifying oxygen prepared by electrolyzing water by green electricity to remove impurities such as hydrogen, carbon monoxide, carbon dioxide and water in the oxygen, then feeding the pure oxygen into the heat exchange system, performing heat exchange liquefaction to obtain liquid oxygen, coupling the liquid oxygen generated by rectification of the air separation rectification system, and obtaining pressurized oxygen through the heat exchange system and the air separation compression and expansion system.