Disclosed is a secondary battery having a constant- voltage device for preventing the secondary battery from being excessively overcharged. The breakdown voltage of the constant- voltage device is lower than the explosion or ignition voltage of the secondary battery, so the discharge operation may occur before the secondary battery is exploded or ignited even if the voltage of the secondary battery rises above the overcharge voltage, thereby protecting the secondary battery from explosion or ignition. The leakage current value of the constant- voltage device is less than 0.05% of the capacity value of the secondary battery under the maximum charge voltage of the secondary battery, or the breakdown voltage of the constant- voltage device is higher than the maximum charge voltage of the secondary battery. Thus, the constant- voltage device rarely generates the leakage current even if the secondary battery has been charged with the maximum charge voltage.