It is an object of the present invention to provide a multistage compressor employing a gas injection system for a CO2 cycle which is able to improve the compression efficiency and the compression performance thereof. In a multistage compressor (2) for a CO2 cycle (1) that carries out two-stage compression by discharging CO2 refrigerant gas compressed in a low-stage side rotary compressing mechanism (4) into a closed housing (3) and taking intermediate pressure refrigerant gas in the closed housing (3) by a high-stage side scroll compressing mechanism (5), a gas injection circuit (15) for injecting intermediate pressure CO2 refrigerant gas extracted from a refrigerant circuit into the closed housing (3) is connected to the closed housing (3), and the pressure ratios of the low-stage side rotary compressing mechanism (4) and the high-stage side scroll compressing mechanism (5) are substantially equivalent, and the ratios of displacement volume are substantially equivalent.