While the safety concerns of lithium-ion batteries have garnered increasing attention due to the frequent accidents in electric vehicles and energy storage stations, fault diagnosis serves as an effective approach to mitigate the potential risks. However, the continuous minor short-circuit (CMSC) fault, with long incubation and unpredictable inducing factors, poses significant challenges for real-time monitoring. To address this problem, a hierarchical quantitative fault diagnosis method is proposed based on M-distance long short-term memory (MD-LSTM) network. First, the M-distance is extracted from the battery module constant current (CC) charging voltage curves, which captures the two characteristics of the charging plateau hysteresis and the voltage sequential difference (VD) reduction. Then, a two-layer LSTM network is established for the hierarchical quantitative diagnosis of CMSC fault. Experimental validation demonstrates that the proposed method achieves a fault detecting accuracy (FDA) of near 100% and a fault classification accuracy of 99.6%, which are about 60.9% and 64% higher than the conventional methods, respectively.