The invention discloses a method for screening an N-k fault set of a power system rapidly. In the prior art, only safety margin, for eliminating all N-1 faults and the part of N-2 faults, of the system is guaranteed based on existing static safety and stability checking; however, with consideration of economy and practical calculation difficulty, potential risks that can not be checked still need to be studied. According to the method provided by the invention, on the basis of definition of a large initial element fault screening scale, a fault set including a key element is found out rapidly by using a system major fault triggering situation as a standard, so that a searching range in the set narrows down further; and the operation is carried out until an N-k fault set meeting the requirement is localized finally. According to the method provided by the invention, unnecessary sampling can be avoided to the great extent. Further precise screening is carried out on the high-capacity screening sample obtained by preliminary screening, so that the calculation complexity is lower than that of the Monte-Carlo-algorithm-based global random screening method obviously and the calculation efficiency is improved. Besides, traversal sampling is avoided to reducing the calculation load.