This paper proposes a new method to identify the vulnerable lines in power grids and predicts the cascading failure path by constructing a cascading failure model of power grids. The line vulnerability index (LVI) of power grids based on line degree and line overload risk is firstly proposed. Then, a cascading failure model of power grids based on LVI is presented while overload emergency control strategy is employed to reduce generation and load powers. Roulette algorithm is used to select sub-fault lines. Finally, the model is applied to the IEEE 39-bus system for simulation. Based on LVI with different weights, simulation results analyze the impact of cascading failure on power grids structure and power balance. It shows that the grid cascading failure model based on the proposed line vulnerability index can simulate the process of cascading failure, comprehensively identify the vulnerable lines of power grid and accurately predict the path of cascading failure.