In recent years, the power system large-scale blackouts have occurred, and the cascading failures become an important cause leading to it. So it is of important guiding significance for the prevention of large-scale blackouts to quickly and accurately forecast the cascading failure possible paths. As for the overload oriented development model of cascading failures featured by relevance between adjacent failure links, relevance indicator is defined, and a method of fast forecasting for power system cascading failures based on failure path tree is proposed. The method uses fuzzy C-means to classify the relevance indicator, selecting the branches with the highest value of relevance indicator as the next failure branch. It effectively reduces the computational load, and overcomes the shortcomings of existing methods. Finally, the simulation results of IEEE 39 nodes prove the rapidity and correctness of the proposed forecasting method.