It is vital to detect the safety state and identify faults of the battery pack for the safe operation of electric vehicles. The voltage faults such as over-voltage and under-voltage imply more serious battery faults including short-circuit and thermal runaway. The voltage abnormal fluctuation is a warning signal of short-circuit, over-voltage and under-voltage. This paper proposes a scheme of three-layer fault detection method for lithium-ion batteries based on statistical analysis. The first layer fault detection is based on the thresholds of over-charge and over-discharge of a battery pack. In the second layer, confidence interval estimation is applied to identify risky cells. In the third layer, correlation and variability of all cells in one battery pack are analyzed by using an improved K-means method to identify abnormal voltage fluctuation over a certain period. The validity and feasibility of the proposed method are verified by real vehicle data from the National Big Data Alliance of New Energy Vehicles.