As one of the key state parameters of the battery, state of health (SOH) represents the degrees of battery degradation, which is very significant for predicting of battery failure and avoiding unsafe behavior of the battery. The difficulty is to determine the appropriate and high correlation input, and design an appropriate estimation algorithm. Through the study of existing battery aging datasets, it is found that the voltage data during charging is relatively stable, which are regular changes with the aging of lithium-ion batteries. Therefore, the voltage data in the charging process were used as the input for estimating SOH, and under the framework of data-driving, an SOH method based on Recurrent Neural Networks with Gated Recurrent Unit (GRU-RNN) was introduced, which could establish the mapping relations between the time series features of one-dimensional voltage data and SOH. The experimental results on two public battery aging datasets show that the proposed method achieves a mean absolute error of 1.25% and a maximum error of less than 5.62%, which is higher than the existing SOH estimation methods in estimation accuracy.