Document-level event causality identification (ECI) aims to detect causal relations in between event mentions in a document. Some recent approaches model diverse connections in between events, such as syntactic dependency and etc., with a graph neural network for event node representation learning. However, not all such connections contribute to augment node representation for causality identification. We argue that the events' causal relations in a document are often interdependent, i.e., multiple causes with one effect, and identifying one cause for an effect may facilitate the identification of another cause of the same effect. In this paper, we use a hypergraph to model such events' causal relations as the document causal structure, and propose a neural causal hypergraph model (NCHM) for event causality identification. In NCHM, we design a pairwise event semantics learning module (PES) based on prompt learning to learn the pairwise event representation as well as the pairwise causal connections between two events. A document causal hypergraph is then constructed based on pairwise causal connections. We also design a document causal structure learning module (DCS) with a hypergraph convolutional neural network to learn document-wise events' representations. Finally, two kinds of representations are concatenated for document-level event causality identification. Experiments on both EventStoryLine and English-MECI corpus show that our NCHM significantly outperforms the state-of-the-art algorithms.