Calculating the basic event probabilities of failure trees is a heavy difficulty in FTA (failure tree analysis) of grinding wheel rack system of CNC (computer numerical control) grinder, because basic events are fuzzy and it is almost impossible to get enough reliability data by experiments with limited time and cost. In order to solve the problem, the fuzzy set theory was introduced and trapezoidal fuzzy numbers were utilized to describe the occurrence probabilities of basic event and top event in FTA. Firstly, the hierarchical structure of grinding wheel rack system of CNC grinder was analyzed, and the failure tree of grinding wheel rack system was established. Then, FFTA (fuzzy failure tree analysis) was made to calculate the trapezoidal fuzzy numbers of occurrence probability of top event by taking the spindle vibration sound of grinding wheel rack system as an example. According to the concept of critical importance in traditional FTA, the fuzzy critical importance for FFTA was firstly defined. Finally, the basic events were ranked according to the fuzzy critical importance, and the basic events with high degree of harm were determined. The results were consistent with the actual situation of the enterprise. The results indicate that this method can effectively solve the problem of confirming accuracy numerical value in FTA of CNC grinder, and provide quantitative calculating evidence to enhance mechanical system reliability for enterprise.