Learning hash functions have been widely applied for large-scale image retrieval. Existing methods usually use CNNs to process an entire image at once, which is efficient for single-label images but not for multi-label images. First, these methods cannot fully exploit independent features of different objects in one image, resulting in some small object features with important information being ignored. Second, the methods cannot capture different semantic information from dependency relations among objects. Third, the existing methods ignore the impacts of imbalance between hard and easy training pairs, resulting in suboptimal hash codes. To address these issues, we propose a novel deep hashing method, termed multi-label hashing for dependency relations among multiple objectives (DRMH). We first utilize an object detection network to extract object feature representations to avoid ignoring small object features and then fuse object visual features with position features and further capture dependency relations among objects using a self-attention mechanism. In addition, we design a weighted pairwise hash loss to solve the imbalance problem between hard and easy training pairs. Extensive experiments are conducted on multi-label datasets and zero-shot datasets, and the proposed DRMH outperforms many state-of-the-art hashing methods with respect to different evaluation metrics.