Accurate battery capacity estimation is crucial for ensuring battery management systems' safe and reliable operation. Although deep learning algorithms have been widely applied in the field of image recognition, their application in battery diagnosis is relatively limited. Besides, obtaining complete cycling data during charging/discharging processes can be challenging in practical applications. This paper proposes a battery capacity estimation method based on partial charge curves and pruned residual neural networks. To leverage the aging information inherent in partial charge curves, the partial segment battery data is transformed into images using wavelet denoising and soft dynamic time warping algorithms. Subsequently, we present a stratified random sampling method to address the issue of imbalanced sample distributions in battery dataset partitioning, and employ residual neural networks to mitigate performance degradation caused by stacking multiple network layers. To validate the effectiveness of the proposed method, experiments are conducted on three types of battery data. During the experimental phase, the root mean square error and mean absolute error of estimated battery capacity are both below 0.79% and 0.54%. Furthermore, a hybrid-pruning algorithm is proposed to enable the deployment of the model on the battery management system, which reduces the model size and computational complexity without compromising accuracy. Compared to other pruning algorithms, the proposed hybrid-pruning algorithm outperforms diagnostic accuracy and computational efficiency after fine-tuning, reducing the model size by 77.40% and creating a more compact structure.