A continuously variable V-belt transmission basically has a driving pulley, a driven pulley and a V-belt wound around the pulleys. The frictional engagement between the pulleys and the V-belt is controlled by regulating pulley axial thrusts to the pulleys. The V-belt has a plurality of torque transmitting connected by an annular ring. A boundary-detection arrangement is provided to detect a boundary position between a first region, in which the elements are arranged without any gap therebetween, and a second region, in which the elements are arranged with a gap therebetween, along a portion of the driving pulley when torque is being transmitted. The detected boundary position is used to estimate the pulley axial thrust applied by the driving pulley against the V-belt, and to control the pulley axial thrust to a lower limit which ensures that the V-belt will not slip upon application of the maximum torque.