Battery state-of-health (SoH) estimation is a critical function in a well-designed battery management system (BMS). In this paper, the battery SoH is detected based on the dynamic characteristic of the charging current during the constant-voltage (CV) period. Firstly, according to the preliminary analysis of the battery test data, the time constant of CV charging current is proved to be a robust characteristic parameter related to the battery aging. Secondly, the detailed expression of the current time constant is derived based on the first order equivalent circuit model (ECM). Thirdly, the quantitative correlation between the normalized battery capacity and the current time constant is established to indicate the battery SoH. Specifically, for the uncompleted CV charging process, the logarithmic function-based current time constant prediction model and the reference correlation curve are established to identify the battery capacity fading. At last, experimental results showed that regardless of the adopted data size, the correlation identified from one battery can be used to indicate the SoH of other three batteries within 2.5% error bound except a few outliers.