Knowledge graph (KG) completion, a cornerstone of semantic reasoning and AI applications, overwhelming majority of them only consider learning from binary relations. Real-world knowledge is inherently N-ary, over 61% of relations in Freebase involve three or more entities. Hypergraphs can effectively model N-ary relations, while existing approaches treat hyperedges as undirected connections and propagating the information of all entities equally, which leads two limitations: (1) Confusing the direction of knowledge flows, resulting in the absence of causal chain reasoning logic. (2) This undirectedness critically harms entities of lower degree ( \({<}3\) neighbors), which suffer from irrelevant information aggregation and incomplete context integration. To resolve these limitations, we propose Direction-aware Attentive Hypergraph (DAHG) network, which resolve the dual challenges through direction-aware hyperedges that preserve the direction of knowledge flows and capture implicit interaction information with global context that inject into lower degree entities. We demonstrate comparative experiments on two benchmark knowledge graph datasets (WN18NN and FB5K-237), that DAHG outperforms the other state-of-the-art completion method, thereby demonstrating its ability to express N-ary directed knowledge effectively.