Accurately predicting the remaining useful life of lithium-ion batteries is crucial for enhancing battery reliability and reducing maintenance costs. In recent years, similarity-based prediction methods have gained significant attention and practical use. However, these methods rely on sufficient and diverse run-to-failure data. To address this limitation, this paper proposes a data augmentation-based SBP method for accurate RUL prediction of lithium-ion batteries. By employing the single exponential model and Sobol sampling, realistic degradation trajectories can be generated, even with only one complete run-to-failure degradation dataset. The similarity between the generated prediction reference trajectories and real degradation trajectories is evaluated using the Pearson distance, and RUL point estimation is performed through weighted averaging. Furthermore, the uncertainty of the RUL predictions is quantified using kernel density estimation. The effectiveness of the proposed RUL prediction method is validated using the NASA lithium-ion battery dataset.