Graph Attention Networks serve as prevalent models for knowledge graph link prediction, enabling the completion of link prediction tasks on general knowledge graphs. However, most current models embed nodes in Euclidean space, leading to distortion in node embedding features. Additionally, existing methods overlook the issue of assigning weights to n-hop neighbors during node embedding aggregation and fail to investigate the prediction of different relation patterns in hyperbolic space. In this paper, we propose a Hyperbolic Graph Attenuated Attenuation Network (HGAAT) model for link prediction, utilizing hyperbolic graph attention networks to handle relations and entity representations in knowledge graphs. By introducing a attenuated attention mechanism, HGAAT effectively integrates information from n-top neighboring nodes, thereby generating more accurate entity and relation embeddings in complex relational graphs. Extensive experiments demonstrate the effectiveness and superiority of the HGAAT model in knowledge graph link prediction tasks.