<p>Accurate and robust remaining useful life (RUL) prediction of lithium-ion battery packs is critical for ensuring system operation reliability and safety. However, the inconsistency accelerates battery pack degradation, making RUL prediction challenging. Furthermore, traditional prediction methods offering specific values cannot meet varying safety and urgency requirements. Aiming at the above problems, this study proposed an RUL interval prediction scheme considering cell inconsistency for lithium-ion battery packs. First, the degradation and inconsistency information of the battery pack is captured by extracting health indicators from the measured data. Second, fuzzy information granulation is introduced to transform the time series data into fuzzy granules, providing upper and lower bounds for interval prediction modeling. Then, long short-term memory is employed for modeling, generating interval prediction results that support decision adjustment for different safety and emergency levels. Finally, the experiment results show that the proposed strategy can effectively cover the real value and achieve reliable interval prediction. It also indicates that the impact of inconsistency on the prediction results becomes more remarkable as the starting point moves back. With 60% training data, the interval prediction evaluation criterion <i>P</i> of the model with inconsistency information is approximately 43% higher than the model without.</p>