An electric power supply system for a vehicle includes a first battery, a second battery connected in parallel with the first battery, a voltage sensor configured to detect a voltage value of the second battery, a current sensor configured to detect a current value of the second battery, an electronic control unit configured to make a voltage of the alternator fluctuate according to a predetermined voltage waveform, and calculate internal resistance of the second battery using the voltage value and the current value of the second battery respectively detected by the voltage sensor and the current sensor while the electronic control unit is making the voltage of the alternator fluctuate according to the predetermined voltage waveform.