The key to the safety of electric vehicle charging is the safety of the vehicle and the battery. A safety fault tree for electric vehicle charging was constructed for the charging system composed of individual power batteries, battery management systems (BMS), and battery module. The weak links of the power battery during the charging process of electric vehicles were analyzed using the minimum cut set theory. Furthermore, a safety evaluation index system for electric vehicle charging was constructed. The weight of the index was determined by combining the Analytic Hierarchy Process with whether the event would trigger a fire. The results indicate that increased internal resistance, mechanical abuse, external corrosion, software failures, mechanical vibration, interpolate short-circuiting, and internal corrosion are weak links in electric vehicle charging. This study can provide reference guidance for the fields of electric vehicle charging management.