In Knowledge Graph Completion (KGC), missing knowledge triples are inferred based on known facts in the knowledge base. In recent years, several representation learning models for knowledge reasoning have achieved promising link prediction results, especially those based on graph attention networks and their derivatives. Such models typically leverage local neighborhood information for each node to learn representation vectors of target entities. However, existing knowledge representation models solely focus on entity embeddings and employ straightforward linear transformations to update relationships. Hence, they are unable to effectively explore structured information with different semantics at the entity and relationship levels. To address these issues, a novel Hyper-bolic Hierarchical Attention Network model for Knowledge Graph Completion (HHAN-KGC), is proposed, incorporating the inference capabilities of hyperbolic algorithms for structured data and the learning capabilities of hierarchical attention networks for entities and relationships, jointly extracting feature vectors for entity and relationship layers. The hyperbolic hierarchical attention network consists of a dual-layer attention mechanism and a relationship semantics mechanism , designed to deeply explore hierarchical feature information embedded in local structures. Thus, HHAN-KGC can establish close associations among triples at different semantic levels, ensuring that the learned knowledge representations possess a certain degree of fidelity and effectively aggregate structured information from entity and relationship layers. Experimental results on multiple knowledge graph datasets demonstrate that HHAN-KGC outperforms the current state-of-the-art methods for knowledge graph link prediction.