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 wobble plate is provided with a cylindrical part which extends in the axial direction of a swash plate, and in the relative rotation structure between the swash plate, and the wobble plate and the outer ring, the swash plate is supported to be able to relatively rotate only in relation to the wobble plate via a bearing interposed at least between the cylindrical part and the inner diameter portion of the swash plate, without being supported to be able to rotate relative to the outer ring. With this wobble plate type variable displacement compressor using the specified constant velocity universal joint mechanism, the relative rotation structure between the wobble plate and the outer ring, and the swash plate, can be improved, workability and productivity can be improved, and the cost and weight can be reduced.