Anti-theft device and vehicle including the same

An anti-theft device is driven with power supplied from a first battery that is charged by an engine started by an engine starting motor. A second battery is charged by the first battery and supplies the anti-theft device with electric power when no electric power is supplied from the first battery to the anti-theft device. A controller stops charging to the second battery when voltage supplied to the anti-theft device from the first battery is reduced to less than a first threshold.