Herbs applicability in disease treatment has been verified through experiences over thousands of years. The understanding of herb–disease associations (HDAs) is yet far from complete due to the complicated mechanism inherent in multi-target and multi-component (MTMC) botanical therapeutics. Most of the existing prediction models fail to incorporate the MTMC mechanism. To overcome this problem, we propose a novel dual-channel hypergraph convolutional network, namely HGHDA, for HDA prediction. Technically, HGHDA first adopts an autoencoder to project components and target protein onto a low-dimensional latent space so as to obtain their embeddings by preserving similarity characteristics in their original feature spaces. To model the high-order relations between herbs and their components, we design a channel in HGHDA to encode a hypergraph that describes the high-order patterns of herb-component relations via hypergraph convolution. The other channel in HGHDA is also established in the same way to model the high-order relations between diseases and target proteins. The embeddings of drugs and diseases are then aggregated through our dual-channel network to obtain the prediction results with a scoring function. To evaluate the performance of HGHDA, a series of extensive experiments have been conducted on two benchmark datasets, and the results demonstrate the superiority of HGHDA over the state-of-the-art algorithms proposed for HDA prediction. Besides, our case study on Chuan Xiong and Astragalus membranaceus is a strong indicator to verify the effectiveness of HGHDA, as seven and eight out of the top 10 diseases predicted by HGHDA for Chuan-Xiong and Astragalus-membranaceus, respectively, have been reported in literature.