Convolutional neural networks have significantly boosted the performance of face recognition in recent years due to its high capacity in learning discriminative features. In order to enhance the discriminative power of the deeply learned features, we propose a new supervision signal named marginal loss for deep face recognition. Specifically, the marginal loss simultaneously minimises the intra-class variances as well as maximises the inter-class distances by focusing on the marginal samples. With the joint supervision of softmax loss and marginal loss, we can easily train a robust CNNs to obtain more discriminative deep features. Extensive experiments on several relevant face recognition benchmarks, Labelled Faces in the Wild (LFW), YouTube Faces (YTF), Cross-Age Celebrity Dataset (CACD), Age Database (AgeDB) and MegaFace Challenge, prove the effectiveness of the proposed marginal loss.