Provided is a constant velocity universal joint capable of being smoothly rotated even when a high operating angle is formed and large torque is born and of reducing excessive load applied to the cage so as to strengthen the cage. The constant velocity universal joint includes an outer joint member having an inner spherical surface (1) in which multiple track grooves (2) are formed; an inner joint member having an outer spherical surface (4) in which multiple track grooves (5) paired with the track grooves (2) of the outer joint member are formed; multiple balls (7) interposed between the track grooves (2) of the outer joint member and the track grooves (5) of the inner joint member so as to transmit torque; and a cage (9) interposed between the inner spherical surface (1) of the outer joint member and the outer spherical surface (4) of the inner joint member so as to retain the balls (7). A tapered relief portion (17) retracted with respect to the outer spherical surface (4) is formed with low curvature at a back end portion (4a) of the outer spherical surface (4) of the inner joint member so as to be smoothly continuous with the outer spherical surface (4).