Objective The estimation of the state of health SOH of lithium-ion power batteries has become a research focus. Accurate SOH estimation is crucial for the smooth operation of electric vehicles and the maintenance of lithium batteries. However the complex working principles of lithium-ion power batteries along with their strong nonlinearity and time-varying characteristics make the accurate estimation of SOH challenging. Meanwhile the diversity of battery operating environments and conditions further increases the uncertainty in the SOH degradation of lithium-ion power batteries. Methods A new method for estimating the SOH of lithium-ion power batteries was proposed. The binary multiobjective adaptive fish migration optimization algorithm-support vector regression BMAFMO-SVR was used to estimate the SOH of lithium batteries. This method extracted extreme points as health features from the curves of the absolute differential thermal voltammetry method and the absolute differential heat capacity method. The binary multi-objective adaptive fish migration optimization algorithm was used to optimize the kernel function parameters of support vector regression and finally the optimized support vector regression was used to accurately estimate the SOH. Comparative experiments were conducted on four groups of batteries from the NASA dataset. Results BMAFMO-SVR exhibited high accuracy in SOH estimation with the root mean square error RMSE within 1%. Conclusion This method demonstrates superiority and feasibility in improving the prediction accuracy of the state of health of lithium batteries.