There is an increasing attention on next-item recommendation systems to infer the dynamic user preferences with sequential user interactions. While the semantics of an item can change over time and across users, the item correlations defined by user interactions in the short term can be distilled to capture such change, and help in uncovering the dynamic user preferences. Thus, we are motivated to develop a novel next-item recommendation framework empowered by sequential hypergraphs. Specifically, the framework: (i) adopts hypergraph to represent the short-term item correlations and applies multiple convolutional layers to capture multi-order connections in the hypergraph; (ii) models the connections between different time periods with a residual gating layer; and (iii) is equipped with a fusion layer to incorporate both the dynamic item embedding and short-term user intent to the representation of each interaction before feeding it into the self-attention layer for dynamic user modeling. Through experiments on datasets from the ecommerce sites Amazon and Etsy and the information sharing platform Goodreads, the proposed model can significantly outperform the state-of-the-art in predicting the next interesting item for each user.