An apparatus for balancing a battery pack having an overdischarge prevention function, which balances a charging voltage of each battery cell of a battery pack that includes a plurality of battery cells, the apparatus comprising: a discharge resistor installed on a conductive line connected to both ends of a battery cell in parallel; a charge pump for pumping charges only when a balance control signal of a predetermined frequency is input thereto; a discharge switching unit for connecting the battery cell to the discharge resistor when a driving voltage of an effective voltage level is applied thereto such that the battery cell is discharged; a voltage charging unit including a capacitor charged with the charges pumped by the charge pump and a resistor for discharging the capacitor, the voltage charging unit applying the charging voltage charged in the capacitor to a gate terminal as the driving voltage of the discharge switching unit; and a controller for measuring charging voltages of the plurality of battery cells included in the battery pack to select a battery cell that requires balancing, and applying the balance control signal having a predetermined frequency to the charge pump connected to the selected battery cell to operate the charge pump, wherein when the balance control signal having a predetermined frequency is applied from the controller, the charge pump pumps charges under the condition that an increasing rate of the charging voltage by the charge pumping process is greater than a decreasing rate of the charging voltage by the discharging process. a discharge resistor installed on a conductive line connected to both ends of a battery cell in parallel; a charge pump for pumping charges only when a balance control signal of a predetermined frequency is input thereto; a discharge switching unit for connecting the battery cell to the discharge resistor when a driving voltage of an effective voltage level is applied thereto such that the battery cell is discharged; a voltage charging unit including a capacitor charged with the charges pumped by the charge pump and a resistor for discharging the capacitor, the voltage charging unit applying the charging voltage charged in the capacitor to a gate terminal as the driving voltage of the discharge switching unit; and a voltage charging unit including a capacitor charged with the charges pumped by the charge pump and a resistor for discharging the capacitor, the voltage charging unit applying the charging voltage charged in the capacitor to a gate terminal as the driving voltage of the discharge switching unit; and a controller for measuring charging voltages of the plurality of battery cells included in the battery pack to select a battery cell that requires balancing, and applying the balance control signal having a predetermined frequency to the charge pump connected to the selected battery cell to operate the charge pump, wherein when the balance control signal having a predetermined frequency is applied from the controller, the charge pump pumps charges under the condition that an increasing rate of the charging voltage by the charge pumping process is greater than a decreasing rate of the charging voltage by the discharging process.