This study proposes a novel approach for predicting the State of Health (SoH) and Remaining Useful Life (RUL) of lithium-ion batteries. The low accuracy of SoH and RUL is due to the challenges of establishing effective feature engineering for battery attributes. To address this issue, a SoH and RUL prediction model based on curve compression and CatBoost is proposed. Firstly, an improved threshold selection method based on curvature analysis is introduced to enhance the compression performance of battery attributes under different cycles. Secondly, to ensure that the extracted feature sequences have the same length, spline interpolation and local anomaly factor detection techniques are utilized to fill or eliminate feature points for feature length normalization. Finally, a dynamic time regularization algorithm is applied to calculate the shortest distance between the feature sequence and the original curve to determine the optimal feature length for input into the CatBoost prediction model. The experimental results demonstrate that the proposed approach outperforms other prediction models in the research object dataset, achieving R2 values higher than 0.98 and MSE values around 1 × 10−5. The proposed approach also achieves better prediction results in the validation object dataset, indicating its strong generalization capability. Additionally, the proposed model shows significant robustness by accurately predicting SoH and RUL under noisy environmental conditions. Overall, the proposed model shows significant potential to accurately predict SoH and RUL by efficiently addressing the challenges associated with feature engineering for battery attributes, reducing the impact of background noise on prediction results, and exhibiting strong robustness.