In control apparatus and method for a power supply equipped in an automotive vehicle, the vehicle includes an engine, a starter to start the engine, a battery to reserve the electrical power supplied to the starter, and a generator driven by means of the engine to generate the electrical power to charge the battery, a terminal voltage of the battery is detected in a form of a battery voltage, a charge current flowing into the battery by means of the generator is detected, and a degree of deterioration of the battery is determined on the basis of at least one of the battery voltage detected after the power supply is turned on and before a start of operation of the generator and the charge current detected after the start of operation of the generator.