Considering the possibility and consequence of line disconnection, a method based on vulnerability of line under impact and disconnection consequence is proposed to identify vulnerable lines in power grid. The vulnerability index of line under impact is defined to evaluate the probability of line breaking from two aspects:the power flow impact of other lines on the target line and the toughness of the target line itself to resist impact. The electrical structure and state transfer characteristics of the power grid are considered at the same time, an index set including the importance of electrical structure, the vulnerability index of line disconnection and the voltage offset of node is constructed. Based on the Fuzzy Analytic Hierarchy Process (FAHP) and the improved entropy weight method, a model for evaluating the consequence of line disconnection is established. Comprehensive vulnerability index is defined by combining the vulnerability index of line under impact and the vulnerability index of disconnection consequence to roundly measure the vulnerability degree of lines in power grid. Simulation results of the IEEE39 node system verify the effectiveness of the proposed method. This work is supported by National Natural Science Foundation of China (No. 51577086) and Natural Science Foundation of Jiangsu Province (No. BK20160778).