A multi-stage compressor comprising: a housing having a sealed container shape; a low-stage side compression mechanism and a high-stage side compression mechanism which are installed in the housing; an electric motor configured to drive the low-stage side compression mechanism and the high-stage side compression mechanism, the electric motor being installed in an intermediate pressure zone in the housing; an injection nozzle installed into the housing in a penetrating manner so as to face the electric motor; and a refrigerant supply part configured to extract a gas phase portion and a liquid phase portion of a compressed refrigerant discharged from the high-stage side compression mechanism, and to selectively supply the gas phase portion and the liquid phase portion to the injection nozzle as an injection refrigerant, wherein the refrigerant supply part includes: a first refrigerant supply passage branching from a condensed refrigerant passage and connected to the injection nozzle, the compressed refrigerant, discharged from the high-stage side compression mechanism thus being condensed and cooled, flowing in the condensed refrigerant passage; a second refrigerant supply passage extending from a space above a liquid surface in a gas-liquid separator, and connected to the injection nozzle, the gas-liquid separator separating the compressed refrigerant, discharged from the high-stage side compression mechanism, into a gas and a liquid; an on-off valve configured to open and close the first refrigerant supply passage; a control part configured to control opening and closing of the on-off valve; and a temperature detection part configured to detect a working temperature of the electric motor, and to input the working temperature into the control part, wherein the control part opens the on-off valve upon the working temperature of the electric motor reaching a predetermined threshold temperature. a housing having a sealed container shape; a low-stage side compression mechanism and a high-stage side compression mechanism which are installed in the housing; an electric motor configured to drive the low-stage side compression mechanism and the high-stage side compression mechanism, the electric motor being installed in an intermediate pressure zone in the housing; an injection nozzle installed into the housing in a penetrating manner so as to face the electric motor; and a refrigerant supply part configured to extract a gas phase portion and a liquid phase portion of a compressed refrigerant discharged from the high-stage side compression mechanism, and to selectively supply the gas phase portion and the liquid phase portion to the injection nozzle as an injection refrigerant, wherein the refrigerant supply part includes: a first refrigerant supply passage branching from a condensed refrigerant passage and connected to the injection nozzle, the compressed refrigerant, discharged from the high-stage side compression mechanism thus being condensed and cooled, flowing in the condensed refrigerant passage; a second refrigerant supply passage extending from a space above a liquid surface in a gas-liquid separator, and connected to the injection nozzle, the gas-liquid separator separating the compressed refrigerant, discharged from the high-stage side compression mechanism, into a gas and a liquid; an on-off valve configured to open and close the first refrigerant supply passage; a control part configured to control opening and closing of the on-off valve; and a temperature detection part configured to detect a working temperature of the electric motor, and to input the working temperature into the control part, wherein a first refrigerant supply passage branching from a condensed refrigerant passage and connected to the injection nozzle, the compressed refrigerant, discharged from the high-stage side compression mechanism thus being condensed and cooled, flowing in the condensed refrigerant passage; a second refrigerant supply passage extending from a space above a liquid surface in a gas-liquid separator, and connected to the injection nozzle, the gas-liquid separator separating the compressed refrigerant, discharged from the high-stage side compression mechanism, into a gas and a liquid; an on-off valve configured to open and close the first refrigerant supply passage; a control part configured to control opening and closing of the on-off valve; and a temperature detection part configured to detect a working temperature of the electric motor, and to input the working temperature into the control part, wherein the control part opens the on-off valve upon the working temperature of the electric motor reaching a predetermined threshold temperature.