In order to identify vulnerable lines which lead to cascading failure of power system, the identification model is proposed based on the power law characteristic of the self-organizing critical theory from the perspective of the developing trend of the accident. When line is out of service due to overload or hidden failures in protection system, critical lines causing power system separation can be found based on the island search method, and islands will be processed to be convenient to power flow calculation. The simulation model of power system blackouts is built considering the improved distribution entropy of power flow and the theory of sensitivity analysis to adjust load level, and the OPF model to adjust generator output. Through a lot of simulation and statistics, the power law or power law tail characteristic of loss load of power system can be used to determine whether the system reaches the self-organizing critical state. While the mathematical expectation of loss load is higher, the self-organized critical state is more dangerous, and the risk of cascading failure is higher. The effectiveness of this method in identifying vulnerable lines of power grid has also been verified by simulation results of IEEE 39-bus system. This work is supported by National Natural Science Foundation of China (No. 51277076) and Fundamental Research Funds for the Central Universities (No. 13MS108).