We present a novel Tensor Composition Network (TCN) to predict visual relationships in images. Visual Relationships in subject-predicate-object form provide a more powerful query modality than simple image tags. However Visual Relationship Prediction (VRP) also provides a more challenging test of image understanding than conventional image tagging, and is difficult to learn due to a large label-space and incomplete annotation. The key idea of our TCN is to exploit the low rank property of the visual relationship tensor, so as to leverage correlations within and across objects and relationships, and make a structured prediction of all objects and their relations in an image. To show the effectiveness of our method, we first empirically compare our model with multi-label classification alternatives on VRP, and show that our model outperforms state-of-the-art MLIC methods. We then show that, thanks to our tensor (de)composition layer, our model can predict visual relationships which have not been seen in training dataset. We finally show our TCNs image-level visual relationship prediction provides a simple and efficient mechanism for relation-based image retrieval.