Link prediction is a critical problem in network structure processing. With the prevalence of deep learning, graph-based learning pattern in link prediction has been well-proven to successfully apply. However, existing representation-based computing paradigms retain some lack in processing complex networks: most methods only consider low-order pairwise information or eliminate the direction message, which tends to obtain a sub-optimal representation. To tackle the above challenges, we propose using directed hypergraph to model the real world and design a directed hypergraph neural network framework for data representation learning. Specifically, our work can be concluded into two sophisticated aspects: (1) We define the approximate Laplacian of the directed hypergraph, and further formulate the convolution operation on the directed hypergraph structure, solving the issue of the directed hypergraph structure representation learning. (2) By efficiently learning complex information from directed hypergraphs to obtain high-quality representations, we develop a framework DHGNN for link prediction on directed hypergraph structures. We empirically show that the merit of DHGNN lies in its ability to model complex correlations and encode information effectively of directed hypergraphs. Extensive experiments conducted on multi-field datasets demonstrate the superiority of the proposed DHGNN over various state-of-the-art approaches.