In electric vehicle (EV) applications, constant current constant voltage (CCCV) charging has been widely used for battery charging. Based on the current analysis in constant voltage (CV) charging phase, this article proposes a novel soft short-circuit (SC) fault diagnosis algorithm that achieves simultaneous fault detection and estimation for EV batteries. The proposed algorithm can accurately estimate SC resistance with the limited CV charging data under unknown battery model parameters. It consists of two parts: online parameter identification during the discharging phase and SC fault estimation during the CV charging phase. Specifically, a set-valued ellipsoidal observer is designed to guarantee the inclusion of the actual battery parameters in the equivalent circuit model (ECM) from the EV operation data at every instant of time. Then, the current model during the CV charging phase is established to iteratively update the SC resistance until the absolute value of the error between the estimated current and measured current is smaller than the predefined threshold. Finally, experimental studies of various types of batteries are conducted under different SC resistances to verify the effectiveness of the proposed algorithm.