A natural-gas purification apparatus includes: a compressor that adjusts the pressure of natural gas from the ground; a cooling unit that liquefies and separates a part of natural-gas liquid by cooling the natural gas after the pressure adjustment by the compressor; a heating unit that heats the natural gas after the separation of the part; a carbon-dioxide separation unit that separates carbon dioxide from the natural gas heated by the heating unit; and an arithmetic control device that adjusts and controls at least one of the compressor, the cooling unit, and the heating unit to a value which has been set in advance according to the composition of the natural gas, such that the cooling unit will liquefy and separate the part of the natural-gas liquid in the natural gas and the carbon-dioxide separator maintains the remaining part of the natural-gas liquid in the natural gas in gaseous form.