To ensure the reliability and safety of lithium-ion battery pack operation, it is very important to accurately and robustly predict its remaining useful life (RUL). However, the inconsistency within the battery pack will accelerate the process of degradation, which increases the difficulty of RUL prediction. At the same time, the traditional numerical prediction method is difficult to adapt to the needs of different security and emergency levels. Therefore, this study proposes a scheme combining battery pack inconsistency evaluation and RUL interval prediction. Firstly, based on the voltage and temperature data, multiple health indicators (HI) reflecting the inconsistency of battery pack were extracted. Secondly, the sample entropy method is used to objectively weight these HIs to evaluate the inconsistency of the battery pack. Then, the inconsistency evaluation results were incorporated into the health indicator system and processed by fuzzy information granulation (FIG) to provide upper and lower bounds for interval prediction. Finally, the long-term and short-term memory (LSTM) neural network was used modeling, taking the upper and lower bound sequences processed by FIG as inputs and the upper and lower bound sequences of capacity as outputs, and the point prediction and interval prediction of RUL is achieved. The experimental results show that this strategy can effectively evaluate the inconsistency of battery pack, and the evaluation results are highly correlated with the degree of battery pack degradation. In addition, for the training data at different starting points, the error of point prediction results is controlled within 0.32 Ah, the comprehensive evaluation criterion P for interval prediction is higher than 1.97, indicating the feasibility and effectiveness of the prediction method.