Unpleasant vibration and muffled sound are restrained. A constant velocity universal joint includes an outer joint part having a plurality of track grooves formed on its cylindrical inner circumferential surface and extending in an axial direction, an inner joint part having a plurality of track grooves formed on its spherical outer circumferential surface and extending in the axial direction, six torque transmitting balls, each being put in a ball track formed by a pair of the track groove of the outer joint part and the track groove of the inner joint part, and a cage having pockets for retaining the torque transmitting balls. The center of curvatures of the spherical outer circumferential surface and the center of the spherical inner circumferential surface of the cage are offset by the same distance in the opposite directions along the axis about the center of the joint. A circumferential arrangement of the ball tracks is made with a uniform pitch, and a circumferential arrangement of the pockets of the cage is made with a random and non-uniform pitch of 55° or more.