The state of health (SOH) and remaining useful life (RUL) of lithium-ion batteries are critical indicators for assessing battery reliability and safety management. However, these two indicators are difficult to measure directly, posing a challenge to ensure safe and stable battery operation. This paper proposes a method for estimating SOH and predicting RUL of lithium-ion batteries by charging feature extraction and ridge regression. First, three sets of health feature parameters are extracted from the charging voltage curve. The relationship between these health features and maximum battery capacity is quantitatively evaluated using the correlation analysis method. Then, the ridge regression method is employed to establish the battery aging model and estimate SOH. Meanwhile, a multiscale prediction model is developed to predict changes in health features as the number of charge-discharge cycles increases, combining with the battery aging model to perform multistep SOH estimation for predicting RUL. Finally, the accuracy and adaptability of the proposed method are confirmed by two battery datasets obtained from varying operating conditions. Experimental results demonstrate that the prediction curves can approximate the real values closely, the mean absolute error (MAE) and root mean square error (RMSE) calculations of SOH remain below 0.02, and the maximum absolute error (AE) of RUL is no more than two cycles.