A refrigerant compressor comprising: - a compression unit that is driven by rotation of a drive shaft passing through a center portion, the compression unit including a low-stage compression unit having a low-stage cylinder chamber that draws in and compresses a refrigerant, a high-stage compression unit having a high-stage cylinder chamber (21 a) that draws in and further compresses the refrigerant compressed by the low-stage compression unit, and an interconnecting portion that connects the low-stage cylinder chamber and the high-stage cylinder chamber, the compression unit compressing the refrigerant in two stages such that a change in volume of the low-stage cylinder chamber discharging the refrigerant and a change in volume of the high-stage cylinder chamber drawing in the refrigerant are phase-shifted and a pressure pulsation loss is generated in the interconnecting portion; - a discharge muffler having in the interconnecting portion a ring-shaped discharge muffler space surrounding the drive shaft, the discharge muffler wherein the refrigerant compressed in the low-stage cylinder chamber flows in the discharge muffler space via a discharge port, the refrigerant that has flowed in circulates in the ring-shaped discharge muffler space, and the refrigerant that has circulated in the discharge muffler space flows out to the high-stage cylinder chamber via a communication port; and - a discharge port rear guide; characterized in that the discharge muffler space is configured to provide circulation flow paths in two different directions around the drive shaft, namely a forward direction and a reverse direction, flowing from the discharge port to the communication port in the ring-shaped discharge muffler space defined by the discharge muffler, the discharge port rear guide blocking the cross-section of the circulation flow path in the reverse direction and preventing the refrigerant discharged via the discharge port from flowing in the reverse direction, wherein the refrigerant is prevented from flowing in the reverse direction, so that the refrigerant circulates in the forward direction in the ring-shaped discharge muffler space and the pressure pulsation loss in the interconnecting portion is reduced. - a compression unit that is driven by rotation of a drive shaft passing through a center portion, the compression unit including a low-stage compression unit having a low-stage cylinder chamber that draws in and compresses a refrigerant, a high-stage compression unit having a high-stage cylinder chamber (21 a) that draws in and further compresses the refrigerant compressed by the low-stage compression unit, and an interconnecting portion that connects the low-stage cylinder chamber and the high-stage cylinder chamber, the compression unit compressing the refrigerant in two stages such that a change in volume of the low-stage cylinder chamber discharging the refrigerant and a change in volume of the high-stage cylinder chamber drawing in the refrigerant are phase-shifted and a pressure pulsation loss is generated in the interconnecting portion; - a discharge muffler having in the interconnecting portion a ring-shaped discharge muffler space surrounding the drive shaft, the discharge muffler wherein the refrigerant compressed in the low-stage cylinder chamber flows in the discharge muffler space via a discharge port, the refrigerant that has flowed in circulates in the ring-shaped discharge muffler space, and the refrigerant that has circulated in the discharge muffler space flows out to the high-stage cylinder chamber via a communication port; and - a discharge port rear guide;