Effective identification of the key lines in a power grid plays a significant role in optimizing the structure and reducing the chain failures of power grid. Therefore, a hidden failure model based on the cellular automata theory considering line hidden failures of power grid is proposed. On this basis, a critical line identification method for power grid is proposed which comprehensively considers load capacity of double terminals, line fault frequency and neighbors of line. Taking IEEE39 node system as a numerical example, this paper identifies its critical lines and verifies the rationality and validity of the proposed model of the method by comparison with other methods. The proposed model and method can provide a new reference for power grid cascading failure model and vulnerability assessment. This work is supported by National Natural Science Foundation of China (No. 51307148) and Hunan Education Department Project (No. 16C1543).