Accurate state of health (SOH) estimation is critical to the operation, maintenance, and replacement of lithium-ion batteries (LIBs), which have penetrated almost every aspect of our life. This paper introduces a new approach to accurately estimate the SOH for rechargeable lithium-ion batteries based on the corresponding charging process and long short-term memory recurrent neural network (LSTM-RNN). In order to learn the mapping function without employing battery models and filtering techniques, the LSTM-RNN is initially fed into the health indicators (HIs) extracted from the charging process and trained to encode the dependencies of the related data sequence. Subsequently, the trained LSTM-RNN can properly estimate online SOHs of LIBs using extracted HIs. We experiment on two public datasets for model construction, validation, and comparison. Conclusively, the trained LSTM-RNN achieves an overall root mean square error (RMSE) lower than 1% on the cases with the same discharging current rate and an RMSE of 1.1198% above 80% SOH on another testing case that underwent a different discharging current rate.