A new method of power system vulnerability analysis is proposed, which is based on the scale-free graph of graph theory to evaluate the vulnerability of complex network. A new analytical model of scale-free graph is constructed, all the state variables of the system is treated as a node in a directed graph, and the definition of the relevant parameters and calculation methods are given, to make up for the the deficiency of power grid vulnerability analysis that considers only the network structure and not combines state parameters, thus the grid vulnerabilities can be revealed better. IEEE57 node system is analyzed and calculated, research shows that the proposed method is correct and effective, ensuring the power system planning and design and the safe operating and maintenance.