In a hybrid electric vehicle in which an internal combustion engine and an electric motor/generator are connected via a clutch, the controller performs the following processing before the operation of the internal combustion engine stops in a stationary state of the vehicle while the clutch is engaged. Specifically, it is determined whether or not the clutch can be disengaged within a predetermined time period. If the clutch can be disengaged within a predetermined time period, the clutch is disengaged. If the clutch cannot be disengaged within the predetermined time period, a driving torque of the internal combustion engine is lowered to an engine stoppable torque set in advance while the clutch is engaged. Then, the operation of the internal combustion engine stops. Through this control, it is possible to prevent a vibration sound or an abnormal sound that may be generated when a driver turns off the ignition button.