An apparatus for estimating a state of charge of a battery, the apparatus comprising: a sensing unit configured to measure a voltage and a current of the battery; a current integrating unit configured to calculate a current integration value for a predetermined period, based on the measured current; and a processor operably coupled to the sensing unit and the current integrating unit, characterized in that the processor is configured to: read out, from a memory, a first initial value related to a state of charge of the battery, a second initial value related to overpotential of the battery, and a third initial value related to an error covariance matrix of an extended Kalmann filter; assign the first initial value and the second initial value respectively to a first state variable and a second state variable of a first state equation of the extended Kalmann filter; predict each of the first state variable and the second state variable based on the current integration value, by using the first state equation; determine a process noise covariance matrix of the extended Kalmann filter, based on any one of the first initial value and the predicted first state variable; predict the error covariance matrix based on the third initial value and the determined process noise covariance matrix, by using a second state equation of the extended Kalmann filter; determine a Kalmann gain of the extended Kalmann filter, based on the predicted error covariance matrix; and correct each of the predicted first state variable and the predicted second state variable, based on the determined Kalmann gain and the measured voltage. a sensing unit configured to measure a voltage and a current of the battery; a current integrating unit configured to calculate a current integration value for a predetermined period, based on the measured current; and a processor operably coupled to the sensing unit and the current integrating unit, characterized in that the processor is configured to: read out, from a memory, a first initial value related to a state of charge of the battery, a second initial value related to overpotential of the battery, and a third initial value related to an error covariance matrix of an extended Kalmann filter; assign the first initial value and the second initial value respectively to a first state variable and a second state variable of a first state equation of the extended Kalmann filter; predict each of the first state variable and the second state variable based on the current integration value, by using the first state equation; determine a process noise covariance matrix of the extended Kalmann filter, based on any one of the first initial value and the predicted first state variable; predict the error covariance matrix based on the third initial value and the determined process noise covariance matrix, by using a second state equation of the extended Kalmann filter; determine a Kalmann gain of the extended Kalmann filter, based on the predicted error covariance matrix; and correct each of the predicted first state variable and the predicted second state variable, based on the determined Kalmann gain and the measured voltage. read out, from a memory, a first initial value related to a state of charge of the battery, a second initial value related to overpotential of the battery, and a third initial value related to an error covariance matrix of an extended Kalmann filter; assign the first initial value and the second initial value respectively to a first state variable and a second state variable of a first state equation of the extended Kalmann filter; predict each of the first state variable and the second state variable based on the current integration value, by using the first state equation; determine a process noise covariance matrix of the extended Kalmann filter, based on any one of the first initial value and the predicted first state variable; predict the error covariance matrix based on the third initial value and the determined process noise covariance matrix, by using a second state equation of the extended Kalmann filter; determine a Kalmann gain of the extended Kalmann filter, based on the predicted error covariance matrix; and correct each of the predicted first state variable and the predicted second state variable, based on the determined Kalmann gain and the measured voltage.