Current sensor fault diagnostic is critical to the safety of lithium-ion batteries (LIBs) to prevent over-charging and over-discharging. Motivated by this, this article proposes a novel residual statistics-based diagnostic method to detect two typical types of sensor faults, leveraging only the 50 current-voltage samples at the startup phase of the LIB system. In particular, the load current is estimated by using particle swarm optimization (PSO)-based model matching with measurable initial system states. The estimation residuals are analyzed statistically with Monte-Carlo simulation, from which an empirical residual threshold is generated and used for accurate current sensor fault diagnostic. The residual evaluation process is well proved with high robustness to the measurement noises and modeling uncertainties. The proposed method is validated experimentally to be effective in current sensor fault diagnosis with low miss alarm rate (MAR) and false alarm rate (FAR).