Learning the distance metric between pairs of examples is of great importance for visual recognition, especially for person re-identification (Re-Id). Recently, the contrastive and triplet loss are proposed to enhance the discriminative power of the deeply learned features, and have achieved remarkable success. As can be seen, either the contrastive or triplet loss is just one special case of the Euclidean distance relationships among these training samples. Therefore, we propose a structured graph Laplacian embedding algorithm, which can formulate all these structured distance relationships into the graph Laplacian form. The proposed method can take full advantages of the structured distance relationships among these training samples, with the constructed complete graph. Besides, this formulation makes our method easy-to-implement and super-effective. When embedding the proposed algorithm with the softmax loss for the CNN training, our method can obtain much more robust and discriminative deep features with inter-personal dispersion and intra-personal compactness, which is essential to person Re-Id. We illustrate the effectiveness of our proposed method on top of three popular networks, namely AlexNet, DGDNet and ResNet50, on recent four widely used Re-Id benchmark datasets. Our proposed method achieves state-of-the-art performances.