In a parallel-connected battery group (PCBG), capacity degradation is usually caused by the inconsistency between a faulty cell and other normal cells, and the inconsistency occurs due to two potential causes: an aging inconsistency fault or a loose contacting fault. In this paper, a novel method is proposed to perform online and real-time capacity fault diagnosis for PCBGs. Firstly, based on the analysis of parameter variation characteristics of a PCBG with different fault causes, it is found that PCBG resistance can be taken as an indicator for both seeking the faulty PCBG and distinguishing the fault causes. On one hand, the faulty PCBG can be identified by comparing the PCBG resistance among PCBGs; on the other hand, two fault causes can be distinguished by comparing the variance of the PCBG resistances. Furthermore, for online applications, a novel recursive-least-squares algorithm with restricted memory and constraint (RLSRMC), in which the constraint is added to eliminate the “imaginary number” phenomena of parameters, is developed and used in PCBG resistance identification. Lastly, fault simulation and validation results demonstrate that the proposed methods have good accuracy and reliability.