The goal of person re-identification (Re-Id) is to match pedestrians captured from multiple non-overlapping cameras. In this paper, we propose a novel dictionary learning based method with the ranking metric embedded, for person Re-Id. A new and essential ranking graph Laplacian term is introduced, which minimizes the intra-personal compactness and maximizes the inter-personal dispersion in the objective. Different from the traditional dictionary learning based approaches and their extensions, which just use the same or not information, our proposed method can explore the ranking relationship among the person images, which is essential for such retrieval related tasks. Simultaneously, one distance measurement has been explicitly learned in the model to further improve the performance. Since we have reformulated these ranking constraints into the graph Laplacian form, the proposed method is easy-to-implement but effective. We conduct extensive experiments on three widely used person Re-Id benchmark datasets, and achieve state-of-the-art performances.