A control apparatus for a vehicle provided with (a) a transmission and (b) a shifting device including (b-1) a shift actuator and (b-2) a shift lever. The shift actuator establishes one of shift ranges in the transmission such that the established one of the shift ranges corresponds to a selected one of shift-lever operating positions of the shift lever. When a switching request is made to request the transmission to be switched to an opposite-direction drive range that is for driving the vehicle in a direction opposite to a current running direction of the vehicle, during running of the vehicle with a speed being not lower than a given value, the control apparatus rejects the switching request. The control apparatus rejects the switching request, also during running of the vehicle with the running speed being lower than the given value, if the vehicle is running on a downhill road.