A control device for a vehicle including an engine stop and start device includes a battery and a vehicle speed detecting unit and includes a battery current detecting unit, a battery temperature detecting unit, a deceleration state detecting unit, a fuel supply stop unit, an average charging current calculating unit, and an SOC estimating unit. The control device calculates, with the average charging current calculating unit, an average of a battery current in a predetermined time from detection of a stop of fuel supply to an engine in a deceleration state of the vehicle. The control device permits a stop of the engine when an SOC calculated by the SOC estimating unit is larger than a predetermined value.