Person re-identification (Re-ID) has become an intense research area in recent years. The main goal of this topic is to recognize and match individuals over time at the same or different locations. This task is challenging due to the variation of illumination, viewpoints, pedestrians’ appearance and partial occlusion. Previous works mainly focus on finding robust features and metric learning. Many metric learning methods convert the Re-ID problem to a matrix decomposition problem by Fisher discriminant analysis (FDA). Mahalanobis distance metric learning is a popular method to measure similarity; however, since directly extracted descriptors usually have high dimensionality, it’s intractable to learn a high-dimensional semi-positive definite (SPD) matrix. Dimensionality reduction is used to project high-dimensional descriptors to a lower-dimensional space while preserving those discriminative information. In this paper, the kernel Fisher discriminant analysis (KLFDA) [38] is used to reduce dimensionality given that kernelization method can greatly improve Re-ID performance for nonlinearity. Inspired by [47], an SPD matrix is then learned on lower-dimensional descriptors based on the limitation that the maximum intraclass distance is at least one unit smaller than the minimum interclass distance. This method is proved to have excellent performance compared with other advanced metric learning.