A swash plate type compressor has a rotary shaft, an inclined swash plate for rotation with the shaft, and a plurality of pistons connected to the swash plate. Each piston defines at both ends thereof a pair of working chambers. The piston reciprocates while being subjected to a swing motion concomitant with the rotation of the swash plate, to suck a fluid into the working chambers for compression. The swash plate is mounted on the shaft through a support unit which serves to selectively vary the inclination of the swash plate and shift the center of rotation of the swash plate along the shaft. The fluid is introduced from a suction passage through and around the swash plate to suction chambers formed adjacent the working chambers. A bypass passage is formed to directly communicate the suction passage with the suction chamber on one side of the shaft while bypassing the swash plate. When the inclination of the swash plate is decreased and the rotational center position thereof is shifted so that substantially no compression of fluid is completed in the working chambers on the one side of the shaft to decrease the displacement of the compressor, the fluid flows in the one side suction chamber through the bypass passage responsively to the flow of fluid toward another side working chambers to lubricate and cool sliding parts for the shaft.