Disclosed is a wobble plate type variable displacement compressor that uses a constant velocity universal joint mechanism, which comprises an inner ring and an outer ring, balls that are held between guide grooves of the inner ring and the outer ring to transmit power, wherein a wobble plate is connected and fixed to the outer ring. In the compressor, the connecting structure for the outer ring and the wobble plate is formed by providing a plurality of concave portions arranged in a circumferential direction on one member, by plastically deforming the other member partially at locations corresponding to the concave portions such that it fits into the concave portions, and by fixing both members to each other in the axial direction and in the rotational direction by means of the plastic deformation. With this wobble plate type variable displacement compressor using the specified constant velocity universal joint mechanism, the structure for connecting the wobble plate and the outer ring in the wobble plate rotation preventing mechanism can be improved, thereby improving the productivity and reducing the cost and the weight.