A compressor reciprocates pistons via a wabble plate wabbled while being prevented from rotating. A wabble plate rotation preventing mechanism is constructed as a mechanism comprising an inner ring axially movable relative to a main shaft, an outer ring connected to the wobble plate, a plurality of balls placed between guide grooves of the inner and outer rings and performing power transmission, and a sleeve axially movably engaged with the inner ring, provided so as to be axially movable together with the inner ring, and functioning as a central member for wabbling of the wabble plate. A difference in shape is provided between the axial cross-sectional profile of a substantially concave spherical surface formed in the inner periphery of the outer ring and the axial cross-sectional profile of a substantially convex spherical surface formed on the outer periphery of the sleeve such that the closer to the axial opposite ends of the contact portion between both the surfaces the position is, the greater the clearance between the surfaces becomes. Seizure and abrasion in sliding sections in the wabble plate rotation preventing mechanism using a specified constant velocity universal joint are suppressed, and a wabble plate type variable displacement compressor exhibiting excellent durability and silent performance can be provided.