Abstract: Deep learning methods have achieved remarkable progress in point cloud completion tasks due to their fast inference and good generalization capabilities. However, existing methods pay less attention to the local geometric information of point clouds, such as normal vectors, vector angles, and higher-order relationships. To address this issue, this paper proposes a geometric point cloud completion network based on hypergraph convolution to generate detailed and complete point clouds. The framework mainly consists of two core components: a geometric feature extractor and a coarse generation module based on hypergraph convolution. Specifically, the former fully extracts the normal vectors, the difference vectors between the center points and the sampled points, and their angles, and integrates them as position encodings into the Transformer structure, enabling the encoder to more fully learn the geometric characteristics and rotation-invariant features of the point cloud. Additionally, in the coarse generation module based on hypergraph convolution, by introducing hypergraph modeling to capture the higher-order correlations between points and using the cross-attention mechanism to explore the interaction between per-point features and higher-order neighborhood features. It guides the generation of point clouds with more geometric structural rationality. Extensive experimental results on multiple datasets verify that the proposed method has superior performance.