Nonlinear degradation prediction of lithium -ion batteries is of great value in battery management systems. Knee point in degradation is a significant signal for state of health. However, large data generated by diverse aging mechanisms and dynamic operating conditions cannot be used completely in prediction. Firstly, this paper proposes a novel data -driven discrete grey model for battery degradation with knee point based on small sample modeling. Secondly, combined with four non -numerical differential methods, knee point is identified according to the predicted degradation trajectory. Then, batteries in 24 different fast charging modes are selected as a set of experimental subjects. Results show that 40% data of total cycles is sufficient to effectively predict battery degradation trajectory and identify the knee point. Finally, performance of fast charging modes is analyzed based on the predicted knee point. This work demonstrates the strong applicability of the grey model in reasonably predicting battery degradation trajectory and accurately identifying the knee point, providing a reference for fast charging schemes in complex engineering systems.