Research on the development mechanism of cascading failure and identification the critical line of evolution path is of great significance for exposing weak links in the power system and reducing the risk of cascading failures. For this reason, an identification method for critical lines of power grid based on fault chain clustering algorithm is proposed. Firstly, an improved direct current power flow simulator of power system separation (DCSS) cascading failure simulation model, which combines with the random chemistry (RC) method to efficiently generate fault chain set with detailed timing information is established. Then, the hierarchical clustering of the failure chain set is realized by using edit distance as the similarity index, and the classified fault chain set can not only reduce the difficulty of subsequent data mining, but also more comprehensively identify the weak links in different cascading failure evolution modes. Finally, taking the Matpower 2 383 node system as an example, the importance of the lines identified by various algorithms is evaluated through the reduction of the system risk level after the expansion of critical lines. The results show that the proposed method can better reduce the risk level of cascading failure, which proves the effectiveness of the proposed model and algorithm.