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How to use hyper-edge to model the multiple association relationship in network data and realize the prediction of potential hyper-edge link relationship has important practical significance. Existing Link prediction methods mainly focus on networks with pairwise relationships. However, directly applying existing link prediction methods to hyper-edge link prediction in hypergraph networks has certain limitations. Therefore, this paper proposed a hyper-edge link prediction model HVGAE（Heterogeneous Variational Hypergraph Autoencoder） based on heterogeneous variational hypergraph autoencoder. Firstly this method used hypergraph convolution to realize variational hypergraph autoencoder, and converted the hypergraph network data into a low-dimension representation. Then it added nodes near-neighbor similarity function to retain the structural information to the largest degree, so as to construct heterogeneous hyper-edge link prediction model. Experiments on three different types of hypergraph networks, the results show that HVGAE model have gained better prediction result compared with that of other baseline methods, indicating that the proposed model can better solve the problem of hyper-edge link prediction in the hypergraph network. [ABSTRACT FROM AUTHOR]