A control system includes a drive source including an engine and a motor. A clutch is provided between the drive source and a driving wheel, wherein the clutch is engaged when a drive range is selected. The system performs, by a speed control of the motor, a control for keeping an input speed of the clutch at a target speed that is equal to the input speed at start of an engagement control of the clutch. The system judges that the clutch has started to be engaged, in response to a condition that a parameter has exceeded a predetermined threshold value when in a start region of the engagement control of the clutch, wherein the parameter changes along with a rotational fluctuation of the drive source. The system starts the judgment after awaiting satisfaction of a predetermined condition after the start of the engagement control of the clutch.