We propose an effective embedding model, named QuatRE, to learn quaternion embeddings for entities and relations in knowledge graphs. QuatRE aims to enhance correlations between head and tail entities given a relation within the Quaternion space with Hamilton product. QuatRE achieves this goal by further associating each relation with two relation-aware quaternion vectors which are used to rotate the head and tail entities' quaternion embeddings, respectively. To obtain the triple score, QuatRE rotates the rotated embedding of the head entity using the normalized quaternion embedding of the relation, followed by a quaternion-inner product with the rotated embedding of the tail entity. Experimental results demonstrate that our QuatRE produces state-of-the-art performances on four well-known benchmark datasets for knowledge graph completion.