In view of the diversification of the existing transient voltage state and the problem that the training speed of a transient voltage stability model needs to be further improved, this paper proposes a method for evaluating the transient voltage stability of AC and DC systems based on voltage trajectory cluster theory and Multiple Between-Class Linear Discriminant Analysis (MBLDA). First, this paper obtains the information of the trajectory clusters of the voltage disturbance of each node of the system after a fault, and establishes the original feature set for transient voltage stability evaluation using the geometric properties of the trajectory clusters. It uses ReliefF to perform feature compression on the original feature set, screens out the subset of features closely related to the transient voltage stability of the system, and effectively represents the four types of transient voltage stability status (fast recovery, delayed recovery, continuous low, and voltage oscillation). Then, the eigenvalue equations of the high-dimensional feature space are transformed into underdetermined homogeneous equations to improve the training speed of the transient voltage stability evaluation model. Then we establish the mapping relationship between the large-scale system voltage feature set and the four transient voltage stability states. Finally, the feasibility and effectiveness of the proposed method are verified by simulation analysis of the modified IEEE-39 node system and the modified IEEE145 node system. This work is supported by the Science and Technology Project of State Grid Corporation of China (No. 5100- 202099271A-0-0-00).