This paper proposes a vulnerability assessment method for power network based on graph neural network using complex network theory and graph neural network model. First, the eigenvector centrality (EC) in complex network theory is chosen as the measure of power system vulnerability. Second, an unsupervised power network vulnerability assessment model based on graph neural networks is established based on power system topological parameters and operational data. Finally, the trained model is used to obtain the EC value ranking of key nodes in the power network, so that the key nodes in the power network can be identified with high accuracy and efficiency, and the effectiveness of the model is verified by the comparison of the time efficiency of the model and the traditional method.