State-of-charge (SOC), which indicates the remaining capacity at the current cycle, is the key to the driving range prediction of electric vehicles and optimal charge control of rechargeable batteries. In this paper, we propose a combined convolutional neural network (CNN) - long short-term memory (LSTM) network to infer battery SOC from measurable data, such as current, voltage, and temperature. The proposed network shares the merits of both CNN and LSTM networks and can extract both spatial and temporal features from input data. The proposed network is trained using data collected from different discharge profiles, including a dynamic stress test, federal urban driving schedule, and US06 test. The performance of the proposed network is evaluated using data collected from a new combined dynamic loading profile in terms of estimation accuracy and robustness against the unknown initial state. The experimental results show that the proposed CNN-LSTM network well captures the nonlinear relationships between SOC and measurable variables and presents better tracking performance than the LSTM and CNN networks. In case of unknown initial SOCs, the proposed network fast converges to true SOC and, then, presents smooth and accurate results, with maximum mean average error under 1% and maximum root mean square error under 2%. Moreover, the proposed network well learns the influence of ambient temperature and can estimate battery SOC under varying temperatures with maximum mean average error under 1.5% and maximum root mean square error under 2%.