Lithium-ion batteries with more rapid capacity loss or “peculiar degradation paths” are usually hard to completely avoid in production given complex electrochemical systems and diverse failure mechanisms. These “abnormal” batteries typically account for only a small proportion in production, and their degradation paths may be very different from most “normal” batteries in the existing dataset. Therefore, it is difficult to accurately predict their subsequent capacity degradation trends using models trained by the existing dataset. To solve this problem, this paper proposes a novel data augmentation technique based on quantum assimilation to accurately predict the state of health of lithium-ion batteries with peculiar degradation paths. The quantum assimilation algorithm has the outstanding advantage of revealing the distribution of the samples by constructing the potential energy surface of the existing data with a nonlinear Gaussian wave function, which provides a novel feature space for data augmentation. The early-cycle data of newly emerged abnormal samples can also be located on this potential energy surface, and the possible degradation increment of each subsequent cycle can be inferred based on the principle that particles tend to gather at the position with the lowest potential energy. Based on this, possible degradation paths of abnormal samples can be generated to enhance the training dataset and the machine learning model trained using it can better predict the abnormal lithium-ion batteries. The proposed method is verified on an actual lithium-ion battery dataset with mean percentage error of the prediction results less than 0.5%, which is at least 44% lower than that of the other four conventional methods.