Researchers use key classes as starting points for software understanding and maintenance. These key classes may cause a significant security risk to the software if they have defects. Therefore, identifying key classes can improve the reliability and stability of the software. Most of the existing methods are based on non-trainable solutions, which calculate the score of each node according to a certain calculation rule, and cannot fully utilize the structural information available in the software network. To solve these problems, a supervised deep learning method is proposed based on graph neural network technology. First, the project is built as a software network and the network embedding learning method Node2Vec is used to learn the node representation. Then, the node representation is mapped into a score through a simple dense network. Second, the aggregation function of the graph neural networks (GNNs) is improved to aggregate important scores instead of node embedding. The direction and weight information between nodes are also considered when aggregating the scores of neighbor nodes. Finally, the nodes are ranked in descending order according to the predicted score output by the model. To evaluate the effectiveness of the proposed method, it is applied to eight Java open-source software systems. The experimental results show that the proposed method performs better than benchmark methods. In the top 10 key candidates, the proposed method achieves 6.4% higher recall and 3.5% higher precision than the state-of-the-art.