This paper proposes a novel algorithm based on the identification of the most influential lines to speed up the simulation of severe cascading failures in power systems. To this end, we first extend the concept of interaction graph to take into account the impact of hidden failures. Then we devise a PageRank-based algorithm to assess the influence of individual lines, which remarkably facilitates finding such severe cascading failures. Numerical experiments carried out on the New England system show that our algorithm can enhance the efficiency of finding severe blackouts of 1∼2 orders of magnitude.