In an infinite speed ratio transmission comprising a continuously variable transmission (2), reduction gear unit (3) and planetary gear set (5), the speed ratio of the continuously variable transmission (2) is controlled by a step motor (36). A range selected by a selector lever (86) is detected by a sensor (84). When the selected range has changed from a stationary range to one of a forward motion range and a reverse motion range, a microprocessor (80) first drives the step motor (36) to a predetermined position (S48, S54). Subsequently, by driving the step motor (36) to an operating position corresponding to a geared neutral point at which the output rotation speed of the infinite speed ratio transmission is zero (S51, S52, S53, S57, S58, S59), the undesirable effects of hysteresis occurring in a relation between the operating position of the step motor (36) and the speed ratio of the continuously variable transmission (2) according to a torque shift of the continuously variable transmission (2) are avoided.