In this paper, we deal with the application of the fuzzy sets theory to evaluate and estimate the system reliability under the fault tree analysis. We formulate the uncertainty of component reliability to fuzzy sets, and propose a procedure for obtaining the system reliability in case the system structure is described by fault tree. An importance measure of each component is proposed. Computer program for fuzzy fault tree analysis(FFTA) is developed using C language to obtain the system reliability and the component‘s fuzzy importance.