These dominant algorithms to learn a similarity is the metric learning that learns a Mahalanobis Similarity Function (MSF) to estimate the similarity of a pair of persons. However, the MSF only projects a pair of persons into feature difference space and ignores the appearance of each individual. In this study, we proposed to learn a Bidirectional Relationship Similarity Function (BRSF) that greatly strengthens the modeling ability of the similarity function. BRSF not only represents the cross correlation relationship of a pair of persons, but also describes the auto correlation relationship. We use the ideal of the Keep It Simple Straightforward Metric (KISSME) algorithm to learn a similarity function. Specifically, the auto correlation relationship and cross correlation relationship of a pair of sample features are expressed by Gaussian distribution. Finally, by converting the ratio of the final Gaussian distribution into the form of BRSF, we get a similarity function which is robust to the change of background, viewpoint, and posture. The proposed method is demonstrated on two public benchmark datasets including VIPeR and QMUL GRID, and experimental results show that the proposed method achieves excellent re-identification rates compared with other similar algorithms. Moreover, the re-identification results on the VIPeR dataset with half of dataset sampled as training samples are quantitatively analyzed, and the performance of the proposed method achieves a 53.21% at Rank1 (represents the correct matched pair).