A category differentiation method of power grid vulnerable lines is proposed by analyzing the causes of the line vulnerability, considering the emphases of line vulnerability assessment in various system states. The easy-breakdown line and easy-affected line are differentiated to distinguish the source with the intermediate link during cascading failure, and the method is realized by complex network and Theil theory. Firstly, structural relative vulnerability is proposed by tenacity index utilizing line load ratio and power supply capacity to make a distinction between attack difficulty and attack effectiveness. Then, state evaluation model is proposed by the impact Theil entropy and anti-impact Theil entropy considering residue consumptive ability of transmission lines. Finally, comprehensive evaluation model of vulnerable lines is established to realize category identification overall combining the structural relative vulnerability and state evaluation model. Case studies were carried out respectively on the IEEE 39-bus and the IEEE 118-bus test system to demonstrate the validity of the proposed method.