In a shift by wire transmission, a control unit limits the shift position (P, R, N, D, L) to be changed beyond a prescribed shift position depending on an initial shift position and an amount of the movement of the shift member in a single shifting operation. Thereby, even when the shift member is excessively advanced or otherwise improperly advanced, the actually selected shift position can be suitably selected so that an undesired change of the shift position can be avoided. The control unit may also limit the selected shift position to be changed beyond a prescribed shift position depending on a traveling speed of the vehicle so that an improper change in the shift position due to vehicle speed constraints can be avoided by using a simple structure.