Being one of the most expensive components of an electrical power plant, the failures of a power transformer can result in serious power system issues. So fault diagnosis for power transformer is highly important to ensure an uninterrupted power supply. Due to information transmission mistakes as well as arisen errors while processing data in surveying and monitoring state information of transformer, uncertain and incomplete information may be produced. Based on these points, this paper presents an intelligent fault diagnosis method of power transformer using fuzzy fault tree analysis (FTA) and beta distribution for failure possibility estimation. By using the technique we proposed herein, the continuous attribute values are transformed into the fuzzy numbers to give a realistic estimate of failure possibility of a basic event in FTA. Further, it explains a new approach based on Euclidean distance between fuzzy numbers, to rank the basic events in accordance with their Fuzzy Importance Index.