Battery packs are applied in various areas (e.g., electric vehicles, energy storage, space, mining, etc.), which requires the state of health (SOH) to be accurately estimated. Inconsistency, also known as cell variation, is considered a significant evaluation index that greatly affects the degradation of battery pack. This paper proposes a novel joint inconsistency and SOH estimation method under cycling, which fills the gap of joint estimation based on the fast-charging process for electric vehicles. First, fifteen features are extracted from current change points during the partial charging process. Then, a joint estimation system is designed, where fusion weights are obtained by the analytic hierarchy process and multi-scale sample entropy to evaluate inconsistency. A wrapper is used to select the optimal feature subset, and Gaussian process regression is implemented to estimate the SOH. Finally, the estimation performance is assessed by the test data. The results show that the inconsistency evaluation can reflect the aging conditions, and the inconsistency does affect the aging process. The wrapper selection method improves the accuracy of SOH estimation by about 75.8% compared to the traditional filter method when only 10% of data is used for model training. The maximum absolute error and root mean square error are 2.58% and 0.93%, respectively.