To identify the direction of cascading failure efficiently when the power grid blackouts happened, the current betweenness is proposed to find out the vulnerable lines in this paper . The index was established under the model in which power flow transferred along all the possible path ,it considered the maximum current and the topological characteristics of the network. The current betweenness can reflect the characteristics of the actual power grid better than the electrical betweenness. When two kinds of attack occur to the IEEE39-bus system , the difference of the maximal transition capability shows the correctness and rationality of the current betweenness index.