Abstract: Lithium-ion batteries are widely used in electric vehicles and energy storage systems. As a prerequisite for the safe and efficient application of lithium-ion batteries, battery management systems have received extensive attention worldwide. Among these prerequisites, the state of charge (SOC), as the basic parameter of battery management system online application, is crucial for the safe and efficient operation of battery management systems. However, measurement noise decreases the accuracy and robustness of the state of charge estimation. To reduce the impact of noise on the state of charge estimation of lithium-ion batteries, a novel SOC estimation method based on an extreme learning machine and a maximum correlation entropy square root volumetric Kalman filter is proposed in this paper. First, the extreme learning machine is used as the measurement equations of the Kalman filter because of its good generalization and fast running speed, and the voltage and current are selected as the model input; second, on the basis of the gray wolf optimization algorithm, the extreme learning machine hyperparameters are thoroughly optimized to improve the accuracy of the state of charge estimation for lithium-ion batteries; finally, on the basis of the framework of the maximum correlation entropy square root volumetric Kalman filter, a closed-loop estimation is realized to further reduce the state of charge estimation error caused by the measurement noise of voltage and current. The proposed method can simplify the time-consuming parameter adjustment of an extreme learning machine and show superior robustness under low-quality measurement. The proposed method is validated under multiple drive cycles and a wide temperature range to verify its generalization performance. The test results show that the proposed method substantially improves the accuracy of lithium-ion battery state of charge estimation. At the same time, the average running time of the proposed method is only one-third of that of long short memory neural networks and gate recurrent unit neural networks. Under complex driving conditions and a large temperature range, the root mean square error of the proposed method is less than 1%, and the maximum error is less than 3%. Furthermore, two case experiments are performed to evaluate the robustness of the proposed closed-loop estimation approach, and the results obtained when data have an initial state of charge error and measurement noise verify the superior robustness of the proposed approach compared with long short memory neural networks and gate recurrent unit neural networks.