The embedded representation and clustering tasks both play important roles in relational data analysis and mining. Traditional methods mainly employ graph structure to describe relational data, but intuitive pairwise connections among nodes are insufficient to model high-order data in the real-world, such as the relations between proteins and polypeptide chains. Hypergraphs are a generalization of graphs, and hypergraphs can well model high-order data. When modeling relational data in the real world, hypergraphs are often accompanied by node attributes, i.e. attributed hypergraphs. Besides this, how to integrate the structural information and attribute information appropriately is another important task, while has not been investigated systematically. In this paper, we propose Adaptive Hypergraph Auto-Encoder(AHGAE) to learn node embeddings in low-dimensional space. Our method can utilize the high-order relation to generate embedding for clustering. It is composed of two procedures, i.e. the adaptive hypergraph Laplacian smoothing filter and the relational reconstruction auto-encoder. It has the advantage of integrating more complex data relations compared with graph-based methods, which leads to better modeling and clustering performance. The proposed method has been evaluated on hypergraph datasets and benchmark graph datasets. Experimental results and comparison with the state-of-the-art methods have demonstrated the effectiveness of our proposed method.