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State-of-charge (SOC) estimation of lithium-ion battery is a key parameter of the battery management system (BMS). However, SOC cannot be obtained directly. In order to predict SOC accurately, we proposed a recurrent neural network called gated recurrent unit network that is based on genetic algorithm (GA-GRU) in this paper. GA was introduced to optimize the key parameters of the model, which can improve the performance of the proposed network. Furthermore, batteries were tested under four dynamic driving conditions at five temperatures to establish training and testing datasets. Finally, the proposed method was validated on dynamic driving conditions and compared with other deep learning methods. The results show that the proposed method can achieve high accuracy and robustness.