Hypergraphs provide an effective modeling approach for modeling high-order relationships in many real-world datasets. To capture such complex relationships, several hypergraph neural networks have been proposed for learning hypergraph structure, which propagate information from nodes to hyperedges and then from hyperedges back to nodes. However, most existing methods focus on information propagation between hyperedges and nodes, neglecting the interactions among hyperedges themselves. In this paper, we propose HeIHNN, a hyperedge interaction-aware hypergraph neural network, which captures the interactions among hyperedges during the convolution process and introduce a novel mechanism to enhance information flow between hyperedges and nodes. Specifically, HeIHNN integrates the interactions between hyperedges into the hypergraph convolution by constructing a three-stage information propagation process. After propagating information from nodes to hyperedges, we introduce a hyperedge-level convolution to update the hyperedge embeddings. Finally, the embeddings that capture rich information from the interaction among hyperedges will be utilized to update the node embeddings. Additionally, we introduce a hyperedge outlier removal mechanism in the information propagation stages between nodes and hyperedges, which dynamically adjusts the hypergraph structure using the learned embeddings, effectively removing outliers. Extensive experiments conducted on real-world datasets show the competitive performance of HeIHNN compared with state-of-the-art methods.