State of health (SOH) is the ratio of the currently available maximum capacity of the battery to the rated capacity. It is an important index to describe the degradation state of a pure electric vehicle battery and has an important reference value in evaluating the health level of the retired battery and estimating the driving range. In this study, the random forest algorithm is first used to find the most important health factors to lithium-ion batteries based on the dataset released by National Aeronautics and Space Administration (NASA). Then the support vector regression (SVR) algorithm is developed to predict the SOH of a lithium-ion battery. The genetic algorithm-particle swarm optimization (GA-PSO) algorithm is brought forward to optimize the parameter values of the SVR, which could improve the estimation accuracy and convergence speed. The proposed SOH estimation method is applied to four batteries and gets a root mean square error (RMSE) of 0.40% and an average absolute percentage error (MAPE) of 0.56%. In addition, the method is also compared with genetic algorithm-support vector regression (GA-SVR) and particle swarm optimization-support vector regression (PSO-SVR), respectively. The results show that (i) compared with the PSO-SVR method, the proposed method can decrease the average RMSE by 0.10%, and the average MAPE by 0.17%; (ii) compared with the GA-PSO method, number of iterations under the proposed method can be reduced by 7 generations.