The invention provides a vehicle parking apparatus with low cost and high reliability, and a method for parking the vehicle. A transmission includes an engine drive gear train capable of changing a speed of a rotation power transmitted from the engine so as to transmit the resulting rotation power to the wheels and switching a plurality of gear positions, an electric vehicle (EV) drive gear train capable of changing the speed of rotation power transmitted from a motor generator so as to transmit the resulting rotation power to the wheels and switching a plurality of gear positions, and a first switching mechanism capable of connecting and disconnecting between the engine drive gear train and the EV drive gear train. A transmission control device connects the engine and wheels through the engine drive gear train, disconnects the motor generator and the wheels through the EV drive gear train, and disconnects the EV drive gear train and the engine drive gear train through the first switching mechanism, in a case when a vehicle start switch is OFF and a parked state of the vehicle is detected.