An electric power supply system includes a first battery provided in an electric power supply circuit; a second battery provided in the circuit and electrically connected in parallel to the first battery, the second battery being a lithium-ion battery; an electric load provided in the circuit and electrically connected in parallel to the first battery and the second battery; a switch provided in the circuit, and configured to electrically disconnect the second battery from the circuit when the switch is open; and a control device configured to open the switch when an ignition switch is on and an SOC of the first battery is equal to or higher than a prescribed SOC, and to execute an open-circuit voltage acquisition process that acquires an open-circuit voltage of the second battery after a lapse of a prescribed time from a time when the switch is opened.