A back-up control unit of a back-up power source device executes: a battery failure determination process of determining whether or not a battery failure has been detected by a failure detecting unit; when it is determined that battery failure has been detected in the battery failure determination process, a switching instruction determination process for determining, on the basis of an instruction signal from a monitor circuit, whether or not an instruction to switch to a P range has been made by a user; and when it is determined that a switching instruction has been made in the switching instruction determination process, a shifting instruction process for starting power supply from a back-up power source to a shift control unit and instructing the shift control unit to shift to the P range.