An accurate state-of-health (SOH) estimation is vital to guarantee the safety and reliability of a lithium-ion battery management system. In application, the electrical vehicles generally start charging when the battery is at a non-zero state of charge (SOC), which will influence the charging current, voltage and duration, greatly hindering many traditional health features to estimate the SOH. However, the constant voltage charging phase is not limited by the previous non-zero SOC starting charge. In order to overcome the difficulty, a method of estimating the battery SOH based on the information entropy of battery currents of the constant voltage charging phase and charging duration is proposed. Firstly, the time series of charging current data from the constant voltage phase are measured, and then the information entropy of battery currents and charging time are calculated as new indicators. The penalty coefficient and width factor of a support vector machine (SVM) improved by the sparrow search algorithm is utilized to establish the underlying mapping relationships between the current entropy, charging duration and battery SOH. Additionally, the results indicate the adaptability and effectiveness of the proposed approach for a battery pack and cell SOH estimation.