Abstract: The boundary problem of critical transient stability is one of the core issues in evaluating the transient stability of power systems. Accurately characterizing the boundary features of critical transient stability is of great significance for power system transient stability assessment. However, in the current transient stability assessment, it is not possible to give the critical state of power grid accurate judgment, so that the safety assessment of the fuzzy area, this paper used an scale invariant feature transform（SIFT） algorithm for the critical transient stability of the boundary feature extraction and mining. In this paper, firstly, the models and functions of transient stability were introduced to derive the critical transient stability problem. After analyzing the correlation of the source-network features, the source-network state variables which can best represent the stable state of the power grid and are closely related to each other are selected as the input features of the algorithm. The SIFT algorithm was used to match the features of the source-network, and the matching node was constructed by constructing the matching evaluation index. Finally, the proposed algorithm was verified by the IEEE-39 bus system and the Henan power grid simulation example. The results show that this method can effectively identify the critical transient stability state of power grid and provide a strong support for the refined evaluation of power grid.