Rating is a typical user explicit feedback that visually reflects how much a user likes a related item. The (rating) matrix completion is essentially a rating prediction process, which is also a significant problem in recommender systems. Recently, graph neural networks (GNNs) have been widely used in matrix completion, which captures users' preferences over items by formulating a rating matrix as a bipartite graph. However, existing methods are susceptible due to data sparsity and long-tail distribution in real-world scenarios. Moreover, the messaging mechanism of GNNs makes it difficult to capture high-order correlations and constraints between nodes, which are essentially useful in recommendation tasks. To tackle these challenges, we propose a Multi-Channel Hypergraph Contrastive Learning framework for matrix completion, named MHCL. Specifically, MHCL adaptively learns hypergraph structures to capture high-order correlations between nodes and jointly captures local and global collaborative relationships through attention-based cross-view aggregation. Additionally, to consider the magnitude and order information of ratings, we treat different rating subgraphs as different channels, encourage alignment between adjacent ratings, and further achieve the mutual enhancement between different ratings through multi-channel cross-rating contrastive learning. Extensive experiments on five public datasets demonstrate that the proposed method significantly outperforms the current state-of-the-art approaches.