Aiming at the problems that the prediction accuracy of lithium battery health status is not high and the model cannot be updated online, a lithium-ion battery health prediction method based on the online sequential extreme learning machine (OSELM) model is proposed. The health factors with high correlation with battery capacity are obtained from the historical charge and discharge data of lithiumion batteries, and the OSELM model is optimized by goose algorithm (GOOSE-OSELM) to improve the prediction accuracy of the model. At the same time, the Cauchy inverse cumulative distribution operator and tangent flight operator are introduced to improve the goose algorithm to improve the global optimization ability and convergence speed of the model, and form an algorithm model with fast calculation speed and online update. The prediction results of the improved goose algorithm-optimized OSELM model (IGOOSE-OSELM) are compared with those of GOOSE-OSELM, OSELM, back propagation (BP) neural networks, and whale optimization algorithm-least squares support vector machine (WOA-LSSVM). The results show that the goodness of fit values of IGOOSE-OSELM in the three battery datasets are above 0.997, and the root mean square error is less than 0.004 5. Finally, the generalization ability of the model is verified by using the Oxford battery dataset and the NASA battery dataset. The results show that the IGOOSE-OSELM model can accurately predict the health status of the battery, and the model has high robustness and adaptability.