Personalized recommender systems are increasingly important as more content and services become available and users struggle to identify what might interest them. Thanks to the ability for providing rich information, knowledge graphs (KGs) are being incorporated to enhance the recommendation performance and interpretability. To effectively make use of the knowledge graph, we propose a recommendation model in the hyperbolic space, which facilitates the learning of the hierarchical structure of knowledge graphs. Furthermore, a hyperbolic attention network is employed to determine the relative importances of neighboring entities of a certain item. In addition, we propose an adaptive and fine-grained regularization mechanism to adaptively regularize items and their neighboring representations. Via a comparison using three real-world datasets with state-of-the-art methods, we show that the proposed model outperforms the best existing models by 2-16% in terms of NDCG@K on Top-K recommendation.