Fault diagnosis is crucial for ensuring the safe and stable operation of complex systems. Recently, graph convolutional network (GCN)-based fault diagnosis method has emerged as a hot research topic due to its ability to effectively handle the association information inherent in the collected dataset. Regarding the method, a fundamental challenge is the construction of the association graph, conventional construction methods struggle to capture the intricate relationships between nodes with complex coupling. Besides, they operate in an unsupervised learning mode, lacking the ability to evaluate and adjust the constructed graph. To handle this challenge, a novel graph convolutional network-based fault diagnosis method via supervised graph construction and optimization (OHCA-GCN) is proposed. Specifically, the supervised orthogonalized-autoencoder is proposed to construct the association graph. Then, a high-order correlation analysis-based graph optimization strategy is proposed to ensure graph sparsity and alleviate the over-smoothing issue. To validate the effectiveness of the proposed method, experiments are carried out on a pulse rectifier dataset from a hardware-in-the-loop platform. The results show that the proposed method exhibits the excellent diagnostic performance compared with the existing methods.