A power supply for a vehicle, the power supply comprising: a first switching element connected between a positive line and a first node; a second switching element connected between the first node and a second node; a third switching element connected between the second node and a negative line; a first battery having a positive electrode and a negative electrode connected to the first node and the negative line, respectively; a reactor element connected between the positive line and a third node; a second battery having a positive electrode and a negative electrode connected to the third node and the second node, respectively; a smoothing capacitor (C H) connected between the positive line and the negative line; and a controller configured to switch each of the first switching element, the second switching element, and the third switching element between an ON state and an OFF state to switch a connection state of the first battery and the second battery between a series connection state and a parallel connection state, wherein when the first switching element is in the OFF state and the connection state of the first battery and the second battery is switched from the series connection state to the parallel connection state during a switching control, the controller is configured to perform a transition control so that a voltage of the smoothing capacitor (C H) is decreased to the higher of a voltage of the first battery and a voltage of the second battery, and to proceed with the switching control by turning on the first switching element after a diode of the first switching element is energized, the transition control being a control to alternately turn on and turn off the second switching element and the third switching element while making an ON duration of the second switching element shorter and an ON duration of the third switching element longer with passage of time. a first switching element connected between a positive line and a first node; a second switching element connected between the first node and a second node; a third switching element connected between the second node and a negative line; a first battery having a positive electrode and a negative electrode connected to the first node and the negative line, respectively; a reactor element connected between the positive line and a third node; a second battery having a positive electrode and a negative electrode connected to the third node and the second node, respectively; a smoothing capacitor (C H) connected between the positive line and the negative line; and a controller configured to switch each of the first switching element, the second switching element, and the third switching element between an ON state and an OFF state to switch a connection state of the first battery and the second battery between a series connection state and a parallel connection state, wherein when the first switching element is in the OFF state and the connection state of the first battery and the second battery is switched from the series connection state to the parallel connection state during a switching control, the controller is configured to perform a transition control so that a voltage of the smoothing capacitor (C H) is decreased to the higher of a voltage of the first battery and a voltage of the second battery, and to proceed with the switching control by turning on the first switching element after a diode of the first switching element is energized, the transition control being a control to alternately turn on and turn off the second switching element and the third switching element while making an ON duration of the second switching element shorter and an ON duration of the third switching element longer with passage of time.