A multi-stage compressor is provided that reliably prevents liquid compression in a higher stage compression mechanism and also prevents compression efficiency degradation resulting from overheating of injection refrigerant and from the lubricating oil being raised up together with the injection refrigerant. An injection circuit is branched into a plurality of circuits. A first circuit thereof is communicatively connected to an inside space of a closed housing that is at the same side as the higher stage compression mechanism with respect to an electric motor, and a second circuit is communicatively connected to an inside space of the closed housing that is opposite from the higher stage compression mechanism with respect to the electric motor. The first circuit and the second circuit are provided with a switching mechanism for switching the injection circuit to the first circuit or the second circuit according to the dryness of the injection refrigerant.