Because it is necessary for electric vehicle (EV) driver to know the remaining power of the EV battery during driving, thus it is very valuable to research the precise state-of-charge estimation, which can update the residual capacity of battery and prevent the occurrence of overcharge and over discharge phenomenon for battery. As compared with most model-based methods, neural network-based methods can directly use battery surface temperature as the input parameters of the model. In here, the state-of-charge of LiNi0.6Co0.2Mn0.2O2/graphite batteries is estimated using the compound method with improved extended Kalman filter and long short-term memory network. The improved extended Kalman filter algorithm is composed of recursive least square method with forgetting factor algorithm, generalized regression neural network and extended Kalman filter algorithm. For the compound state-of-charge estimation method, the state-of-charge values are first estimated using the improved extended Kalman filter, and then optimized using long short-term memory network. The datasets of dynamic stress test at 25 degrees C are applied to train the long short-term memory network, while the datasets under different conditions are used as validation datasets. The results reveal that the mean absolute error, maximum absolute error, and root mean square error for their combination method are less than 1%, 3%, 1.1%, respectively. Among three kinds of state-of-charge estimation methods, the compound method has the highest estimation accuracy under different working conditions.