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Some critical lines can have important impact on the large-scale blackouts and cascading failures in power grid. Based on the newest progress in the field of complex network, a new vulnerability index called weighted line betweenness is proposed as vulnerability index in this paper. The weighted line betweenness of one line is defined as the sum of the loads acted on this line, which are brought by the shortest electric paths between generator nodes and load nodes that passing through this line. We revise the weighted line betweenness by increasing the betweenness to the highest betweenness in the neighboring lines before revision. Vulnerability analysis has been carried out on the IEEE 39 bus system and Huazhong-Chuanyu power grid. The time domain simulation results verify that the weighted line betweenness can not only identify the most critical lines but also find out those light loaded but critical lines due to their special position in the power grid.