This invention is about a natural gas isobaric liquefaction apparatus, which is based on the Rankine cycle system of similar thermal energy power circulation apparatus at cryogenic side, a cryogenic liquid pump is used to input power and the refrigerant makes up cold to the natural gas liquefying apparatus, so as to realize the isobaric liquefaction of natural gas. The natural gas liquefying apparatus of this invention can save energy by over 30% as compared with the traditional advanced apparatus with the identical refrigerating capacity, therefore it constitutes a breakthrough to the traditional natural gas liquefaction technology, with substantial economic, social and environmental protection benefits.