A multi-stage compression type rotary compressor, having a driving element and a first and a second rotary compression element that are driven by the driving element in a sealed container, is provided. The refrigerant compressed by the first rotary compression element is discharged into the sealed container, and said discharged refrigerant with an intermediate pressure is then compressed by the second rotary compression element. By cooling the refrigerant absorbed into the second rotary compression element, the rise in the temperature of the refrigerant that is compressed and discharged by the second rotary compression element can be suppressed. And, the supercooling degree of the refrigerant is increases before reaching the expansion valve to improve the cooling ability of the evaporator.