Link prediction in knowledge graphs is the most effective method for graph complementation, which can effectively improve the data quality of knowledge graphs. However, the relationships in real life are often multiple, thus these knowledge graphs containing multiple relationships can be called knowledge hypergraphs (KHGs). Unfortunately, the existing knowledge graph link prediction methods cannot be directly applied to knowledge hypergraphs, and the existing knowledge hypergraph link prediction models ignore the equality (there is no sequential relationship among the elements in a multivariate relationship) and completeness (a multivariate relationship is not valid if it lacks elements) of the real-life multivariate relationships. To address these problems, a knowledge hypergraph multivariate representation model is firstly proposed, which can directly model the multivariate relationships in the knowledge hypergraph. Then, a multi-granularity neural network-based hypergraph prediction method (HPMG) is studied, which divides the relations into multiple granularities for learning and prediction from different granularities jointly. Next, to address the problem of inadequate HPMG feature fusion, HPMG⁺ is proposed based on multi-granularity attention network for link prediction of knowledge hypergraphs, which combines all and local attention to achieve differentiated fusion of different features and further improves the performance of the model. Finally, extensive experimental results on real datasets verify that the proposed methods significantly outperform all baseline methods in terms of hyper-edge prediction.