A vehicle driving system comprising: a first battery; a second battery; a drive motor-generator connected to the first battery and the second battery via respective relays; a power receiving unit connected to the first battery and the second battery via respective relays and also connected to an external power supply; and a controller, wherein: the first battery is configured to be permitted to be charged and discharged; the second battery has a higher capacity than the first battery; and the controller is configured to, when the power receiving unit is connected to the external power supply, cause the first battery to be charged if the state of charge of the first battery is lower than a predetermined SOC and cause the second battery to be charged if the state of charge of the first battery is higher than or equal to the predetermined SOC, characterized in that the first battery is configured to be permitted to be charged and discharged at a current rate of higher than or equal to 5C; the controller is configured to cause a charging current value to be higher when the first battery is charged from the power receiving unit than when the second battery is charged from the power receiving unit; and the controller is configured to, when the power receiving unit is connected to the external power supply, cause the first battery to be charged if the state of charge of the first battery is lower than a predetermined SOC regardless of a state of charge of the second battery. a first battery; a second battery; a drive motor-generator connected to the first battery and the second battery via respective relays; a power receiving unit connected to the first battery and the second battery via respective relays and also connected to an external power supply; and a controller, wherein: the first battery is configured to be permitted to be charged and discharged; the second battery has a higher capacity than the first battery; and the controller is configured to, when the power receiving unit is connected to the external power supply, cause the first battery to be charged if the state of charge of the first battery is lower than a predetermined SOC and cause the second battery to be charged if the state of charge of the first battery is higher than or equal to the predetermined SOC, characterized in that the first battery is configured to be permitted to be charged and discharged at a current rate of higher than or equal to 5C; the controller is configured to cause a charging current value to be higher when the first battery is charged from the power receiving unit than when the second battery is charged from the power receiving unit; and the controller is configured to, when the power receiving unit is connected to the external power supply, cause the first battery to be charged if the state of charge of the first battery is lower than a predetermined SOC regardless of a state of charge of the second battery. the first battery is configured to be permitted to be charged and discharged; the second battery has a higher capacity than the first battery; and the controller is configured to, when the power receiving unit is connected to the external power supply, cause the first battery to be charged if the state of charge of the first battery is lower than a predetermined SOC and cause the second battery to be charged if the state of charge of the first battery is higher than or equal to the predetermined SOC, characterized in that the first battery is configured to be permitted to be charged and discharged at a current rate of higher than or equal to 5C; the controller is configured to cause a charging current value to be higher when the first battery is charged from the power receiving unit than when the second battery is charged from the power receiving unit; and the controller is configured to, when the power receiving unit is connected to the external power supply, cause the first battery to be charged if the state of charge of the first battery is lower than a predetermined SOC regardless of a state of charge of the second battery.