Identification of vulnerable lines in power systems has great meaning to predict cascading failures and prevent the blackouts. A novel approach to identify the vulnerable lines in power systems based on the weighted H-index is proposed. Firstly, to remove the Kirchhoff's law constraint in power system, a second-level correlation network is constructed considering the secondary cascading failure. Then, the relative node strength is defined in the second-level correlation network to improve the identification effectiveness. Secondly, a weighted H-index is proposed, aiming at the disadvantages of the classic Hindex only suited for unweighted networks. The improved indicator is applied in the second-level correlation network to identify the vulnerable lines of the power grid. The proposed method is verified in the IEEE-39 bus system and a real-life regional power grid in China. The experimental results show that the proposed method has higher precision compared with other methods. Specifically, the identification accuracy is improved by at least 8.33% than existing methods in the IEEE-39 bus system. In addition, the weighted H-index has higher discrimination and robustness than the classic H-index. INDEX TERMS Vulnerable lines, weighted H-index, second-level correlation network, power system.