NOVELTY - The system has a cooling section for cooling an intermediate supercritical fluid (F1) generated in a compression section to near a critical temperature to generate an intermediate super-critical pressure liquid (F2). A pumping section compresses the liquid generated in the cooling section to pressure that is equal to or higher than target pressure. A heating section heats the liquid compressed in the pumping section to near the critical temperature. The cooling section includes a main cooling part to perform heat exchange with the heating section to cool the intermediate supercritical fluid.    USE - Compressing system for compressing a target gas i.e. carbon dioxide, to a pressure at a thermoelectric power plant.    ADVANTAGE - The system returns gas or supercritical fluid which is heated, evaporated and generated such that low-temperature liquid which is extracted and generated in the extracting and decompression section is not discharged to outside, and a gas or super- critical fluid generated from the low-temperature liquid can be returned to the equivalent pressure part of the compressor equivalent to the pressure of the gas or supercritical fluid, thus reducing power of the system by combining the compression section and the pumping section and cooling the intermediate supercritical fluid in the state of a pressure that is equal to or higher than the critical pressure in the cooling section, and hence providing reliability improvement to the system and efficiency of the overall system. The intermediate supercritical fluid can be pre-cooled by a pre-cooling part, thus reducing amount of refrigeration required by the main cooling part.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a gas compressing method for compressing a target gas to a pressure that is equal to or higher than a target pressure higher than a critical pressure.    DESCRIPTION OF DRAWING(S) - The drawing shows a graph representing a state of carbon dioxide regarding a compressing system.    Intermediate supercritical fluid (F1)    Intermediate super-critical pressure liquid (F2)    Target pressure liquid (F3)    Target supercritical fluid (F4)    Low-temperature liquid (F5)