Given the benefits of its low storage requirements and high retrieval efficiency, hashing has recently received increasing attention. In particular, cross-modal hashing has been widely and successfully used in multimedia similarity search applications. However, almost all existing methods employing cross-modal hashing cannot obtain powerful hash codes due to their ignoring the relative similarity between heterogeneous data that contains richer semantic information, leading to unsatisfactory retrieval performance. In this paper, we propose a tripletbased deep hashing (TDH) network for cross-modal retrieval. First, we utilize the triplet labels, which describes the relative relationships among three instances as supervision in order to capture more general semantic correlations between cross-modal instances. We then establish a loss function from the inter-modal view and the intra-modal view to boost the discriminative abilities of the hash codes. Finally, graph regularization is introduced into our proposed TDH method to preserve the original semantic similarity between hash codes in Hamming space. Experimental results show that our proposed method outperforms several state-of-the-art approaches on two popular cross-modal datasets.