Line electrical betweenness based on DC load flow and a new net efficiency index are proposed to identify the vulnerable lines in the complex power grid. The electrical betweenness not only overcomes the shortcoming of the weighted reactance betweenness which assures that power is transmitted through the shortest or the most effective paths, but also considers the impact of the capacity and distribution of generators and load. A new net efficiency index, which considers electrical distance and capacity distribution, is introduced to measure the efficiency of power grid after attack. Numeric simulation results of IEEE-39 and IEEE-118 show the lines with high electrical betweenness usually belong to long-distance and are the important transmission lines. If these lines are attacked intentionally, the efficiency of power grid would descend rapidly. The results also show that the betweenness index can identify the vulnerable lines in the complex power grid.