Accurate and rapid fault detection is essential for the safe operation of lithium-ion batteries in electric vehicles. However, conventional fault detection methods dependent on constant thresholds may have false alarms or missing alarms due to the inevitable disturbances resulted from the battery system modeling errors and measurement noises. In this paper, we design a multi-objective nonlinear fault detection observer for lithium-ion batteries, which is robust against disturbances but sensitive to battery multi-fault. We then perform formal stability and L∞/H_ performance analysis for the resultant estimation error system. Furthermore, tractable design procedures for the observer gain parameter and an adaptive threshold are derived. Then, via adaptive thresholding, a delicate three-step multi-fault detection scheme is developed to detect the occurrence of battery various faults, including short-circuit faults, current and voltage sensor faults. Finally, the efficacy of the proposed scheme is validated under several experimental case studies involving a variety of faults with their different levels of severity and erroneous SOC initialization.