Person re-identification is the problem of matching pedestrians under different camera views. The goal of person re-identification is to make the truly matched pedestrian pair rank as the first place among all pairs, with the direct translation in math language, which equals that the distance of matched pedestrian pair is the minimum value of the distances of all pairs. In this paper, we propose a novel metric learning method for person re-identification to learn such an optimal feature mapping function, which minimizes the difference between the distance of matched pair and the minimum distance of all pairs, namely Ranking Loss. Furthermore, we develop an improved version of ranking loss by using p-norm as a smooth approximation of minimum function, with the advantage of manipulating parameter p to control the distance margin between matched pair and unmatched pair to benefit the re-identification accuracy. We also present an efficient solver using only a small portion of pairs in computation, achieving almost the same performance as using all. Compared with other loss function, the proposed ranking loss optimizes the ultimate ranking goal in the most direct and intuitional way, and it directly acts on the whole gallery set efficiently instead of comparatively measuring in small subset. The detailed theoretical discussion and experimental comparisons with other loss functions are provided, illustrating the advantages of the proposed ranking loss. Extensive experiments on two datasets also show the effectiveness of the proposed method compared to state-of-the-art methods.