We present a Riemannian discriminative learning framework for multiple-shot person re-identification, named Multiple-shot Riemannian Discriminative Learning (MRDL). Firstly, image regions are encoded into covariance matrices or a Gaussian extension as robust feature descriptors. Since these matrices lie on some specific Riemannian manifolds, we introduce a manifold averaging strategy to fuse the feature descriptors from multiple images for a holistic representation, and exploit Riemannian kernels to implicitly map the averaged matrices to a Reproducing Kernel Hilbert Space (RKHS), where conventional discriminative learning algorithms can be conducted. In particular, we apply kernel variants of two typical methods, i.e., the Linear Discriminant Analysis (LDA) and Metric Learning to Rank (MLR), to demonstrate the flexibility of the framework. Extensive experiments on five public datasets including i-LIDS, CAVIAR, PRID2011, CUHK01 and SPRD exhibit impressive improvements over existing multiple-shot re-identification methods as well as representative single-shot approaches.