This paper proposes a novel idea that a low-rank update algorithm is used to calculate N-k short-circuit current. In the method, the node admittance matrix is revised by the product of two low-rank matrixes that had been constructed. Afterwards according to the originally decomposed admittance matrix factor table and the result of calculation of low-rank matrixes, the revised admittance matrix is avoided to be refactorized, so the amount of calculation is decreased greatly. Since it is not restricted by the quantity of broken branches, the correction computation of broken multi-branches can be finished all at once, which adapts to the requirement of variable operation modes. Comparing with the present methods, the low-rank update method avoids the problem caused by the big calculative amount from reforming factor table due to the modified original admittance matrix, and by the complicated process of calculation in the compensation method due to the recursion when multi-lines are broken synchronously such as breaking three-winding transformer, autotransformer, and multicomponent on bus. Finally, an S-1047 system is employed to analyze the validity and practicality of this proposed method.