Timely and accurate fault diagnosis for a lithium-ion battery pack is critical to ensure its safety. However, the early fault of a battery pack is difficult to detect because of its unobvious fault effect and nonlinear time-varying characteristics. In this paper, a fault diagnosis method based on relative entropy and state of charge (SOC) estimation is proposed to detect fault in lithium-ion batteries. First, the relative entropies of the voltage, temperature and SOC of battery cells are calculated by using a sliding window, and the cumulative sum (CUSUM) test is adopted to achieve fault diagnosis and isolation. Second, the SOC estimation of the short-circuit cell is obtained, and the short-circuit resistance is estimated for a quantitative analysis of the short-circuit fault. Furthermore, the effectiveness of our method is validated by multiple fault tests in a thermally coupled electrochemical battery model. The results show that the proposed method can accurately detect different types of faults and evaluate the short-circuit fault degree by resistance estimation. The voltage/temperature sensor fault is detected at 71 s/58 s after faults have occurred, and a short-circuit fault is diagnosed at 111 s after the fault. In addition, the standard error deviation of short-circuit resistance estimation is less than 0.12 Ω/0.33 Ω for a 5 Ω/10 Ω short-circuit resistor.