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High-order correlation is an important property of hyperspectral images (HSIs) and has been widely investigated in model-based HSI denoising. However, the existing deep learning-based HSI denoising approaches have not fully utilized the high-order correlation. Hypergraph convolutional networks have shown great potential in capturing the high-order correlation. Therefore, in this paper, we propose a novel HSI denoising method by employing hypergraph convolution to characterize the high-order correlation at the patch level. Specifically, our framework is a symmetrically skip-connected 3D encoder–decoder architecture, which enhances the extraction and utilization of local features. Furthermore, to integrate competently the hypergraph convolutional modules into the 3D framework, we devise a dimensional transformation module that facilitates the fusion of 3D convolution and hypergraph convolution. Notably, in the hypergraph convolution operation, we use a data-driven technique to acquire the incidence matrix of a hypergraph, efficiently constructing the HSI into a high-order structure. Our proposed method excels in HSI denoising performance compared to state-of-the-art approaches, evidenced by extensive experiments on synthetic and real-world noisy HSIs. • We propose a novel HSI denoising method based on HGCN. • We present a learning-based technique to acquire the incidence matrix of a hypergraph. • The structure and complexity analysis of the proposed model are discussed. • Our proposed method excels in HSI denoising performance compared to state-of-the-art approaches. [ABSTRACT FROM AUTHOR]