With the growing number of Web services, classifying Web services accurately and efficiently has become a challenging problem. Effective service classification is conducive to improving the quality of service discovery and the efficiency of service composition. Existing graph neural network methods represent the target service node by a weighted sum of the features of the neighbor service nodes, and have achieved remarkable results in service classification. However, these methods ignore the impact of possible interactions between neighbor service nodes on the target service node. To address this problem, we propose a Web services classification method based on bilinear graph neural network. Our proposed method can model the bilinear interactions between neighbor service nodes and effectively improve the accuracy of service classification. First, our proposed model uses the Word2Vec model to extract the latent semantic vectors from service description documents. We then construct the service relationship network according to tags and shared annotation relationships of Web services. Next, a bilinear aggregator is used to model the pairwise interactions between neighbor service nodes, highlighting the local common attributes. Finally, the bilinear aggregator is combined with the weighted sum aggregator to construct a bilinear graph neural network, which can learn more comprehensive representations of services. The experimental results on the real dataset from ProgrammableWeb show that the classification accuracy of the proposed method is greatly improved compared with DeepWalk, Node2Vec, GCN, and GAT.