Because current information is the most crucial factor for the state estimation of battery management systems, it is essential to ensure the accuracy of the current-sensor built into battery systems. However, non-contact current-sensors, which are widely used in battery systems, are sensitive to operational conditions and the environment. The accuracy of the sensor is easily affected by various factors, such as temperature changes or unstable supply voltages. This study proposes a current-sensor error compensation algorithm to overcome the potential inaccuracies caused by various current-sensor faults. This method is based on the dual sigma-point Kalman filter, which enables simultaneous estimation of the internal states of the battery cell and the bias of the current measurement. To verify the effectiveness of the proposed method, three types of possible current-sensor errors step, ramp, and sinusoidal errors were subjected to current measurement. The effectiveness of the proposed algorithm was verified using a cylindrical battery cell, and the experimental results showed that the proposed method could estimate and compensate for all current measurement errors.