Fake news detection is an important research sub-topic in the field of natural language processing and has broad application prospects. Notably, the evidence-based fake news detection task has attracted increasing attention and produced promising results. Despite the successes, current approaches still have limitations. First, they are unable to capture interactions in news articles where long-range dependencies exist and are often accompanied by redundant information. Second, they ignore the existence of multivariate higher-order interactions between claim and evidences in news content and within themselves. To address these issues, in this paper, we propose a HypergraphContrastive Learning (HCL) for evidence-based fake news detection. Specifically, we model claim and evidence as hypergraph data and capture the long-range semantic dependencies between dispersed related parts of the context via a hypergraph neural network. After capturing contextual semantic information, our model learns the correlation between claim and evidence through graph contrastive learning methods to further improve the effectiveness of semantic alignment. Experimental results on two public datasets demonstrate the effectiveness of our method.