In the energy crisis and post-epidemic era, the new energy industry is thriving, encompassing new energy vehicles exclusively powered by lithium-ion batteries. Within the battery management system of these new energy vehicles, the state of charge (SOC) estimation plays a pivotal role. The SOC represents the current state of charge of the lithium-ion battery. This paper proposes a joint estimation algorithm based on genetic algorithm (GA) simulating biogenetic properties and support vector regression (SVR) to improve the prediction accuracy of lithium-ion battery SOC. Genetic algorithm support vector regression (GASVR) is proposed to address the limitations of traditional SVR, which lacks guidance on parameter selection. The model attains notable accuracy. GASVR constructs a set of solution spaces, generating initial populations that adhere to a normal distribution using a stochastic approach. A fitness function calculates the fitness value for each individual. Based on their fitness, the roulette wheel method is employed to generate the next-generation population through selection, crossover, and mutation. After several iterations, individuals with the highest fitness values are identified. These top individuals acquire parameter information, culminating in the training of the final SVR model. The model leverages advanced mathematical techniques to address SOC prediction challenges in the Hilbert space, providing theoretical justification for handling intricate nonlinear problems. Rigorous testing of the model at temperatures ranging from −20 °C to 25 °C under three different working conditions demonstrates its superior accuracy and robustness compared to extreme gradient boosting (XGBoost), random forest regression (RFR), linear kernel function SVR, and the original radial basis kernel function SVR. The model proposed in this paper lays the groundwork and offers a scheme for predicting the SOC within the battery management system of new energy vehicles.