The traction power supply system based on Inductively Coupled Power Transfer (ICPT) technology is one of the new traction power supply technologies that will be developed in the future. As the core part of rail transit energy transfer and conversion, the traction power supply system is not only the critical system for the safe operation of rail transit, but also the main source of its failures, so it is of great significance to study its reliability. In this paper, the reliability analysis of the non-contact traction power supply system based on mobile ICPT technology is carried out using the method of (Fault Tree Analysis) FTA combined with triangular fuzzy theory and grey relational theory. Firstly, the fault tree of the system is established, and the minimum cut sets and structure function of the fault tree are obtained. Then the triangular fuzzy numbers are introduced to represent the probability of the bottom events, and the fuzzy probability of the top event and the fuzzy importance of the bottom events are determined, after that, the maximum probability of failure of the top event is obtained. Finally, the grey relational degrees of each minimum cut set are obtained and ranked. Furthermore, in order to prove the correctness of this method, the trapezoidal fuzzy FTA is introduced and compared with it. Both research results show that the loosely coupled transformer and Insulated Gate Bipolar Transistor (IGBT) module are the weak links of the system. The results obtained are consistent and realistic, which proves the correctness of the method selected in this article.