The safety of LIB (lithium-ion battery) was analyzed by the rheology-mutation theory and FIA (fault tree analysis) method. The explosion process of LIB can be viewed as a rheology-mutation process. The process of safety rheology with time can be divided into three stages: decelerated, stable and accelerated growth stage, respectively. The physical model and mathematic model were built to estimate the probability of LIB explosion based on the rheology-mutation theory. The influence of different parameters, like external force, strength coefficient and wear coefficient, on probability of LIB explosion were discussed. The results showed that the external force is the most important parameter which controls the overall growth trend of the probability of LIB explosion. Strength coefficient determines the resistance of LIB to the external stimulation. Wear coefficient controls the rate of rheology and mutation. The external forces, strength coefficient and wear coefficient were influenced by the factors, which lead to the LIB explosion. In order to analyze these factors, a fault tree of LIB explosion was built. The minimum cut sets and the structure importance degree coefficient of each basic event were calculated through Boolean algebra method. The collision is the most important factor that influences the LIB explosion. The protective measures for the safe use of LIB were proposed. (C) 2017 Elsevier Ltd. All rights reserved.