A multi-piston swash plate type compressor for an air-conditioning system used in a vehicle such as an automobile, including a cylinder block body having a swash plate chamber formed therein for receiving a swash plate and cylinder bores formed therein for receiving pistons which are reciprocated by rotation of the swash plate. The compressor has a suction chamber which is fed with a refrigerant including lubricating oil from an evaporator of the air-conditioning system and a discharge chamber which feeds the compressed refrigerant to a condenser of the air-conditioning system. When the compressed refrigerant is discharged from the cylinder bore into the discharge chamber through a discharge reed valve, all of the discharged refrigerant is impinged on the peripheral and inner wall so as to separate the lubricating oil from the refrigerant, whereby an effective damping and sealing oil layer is formed between the discharge reed valve and the valve seat thereof.