Image-set classification has recently generated great popularity due to widespread application to challenging tasks in computer vision. The great challenges arise from measuring the similarity between image sets which usually exhibit huge inter-class ambiguity and intra-class variation. In this paper, based on the assumption that each image set as a linear subspace can be treated as a point on a Grassmann manifold, we propose discriminant Grassmann kernels (DGK) of principal angles between subspaces. To tackle the ambiguity and variation, we propose learning the DGK via kernel target alignment, which achieves kernels of great discrimination by maximizing correlations with class labels. The proposed DGK has been evaluated on two challenging datasets including the ETH-80 and UCSD datasets for object recognition and video-based traffic congestion recognition, respectively. Extensive experiments have shown that the proposed DGKs achieves state-of-the-art performance and surpasses most of previous methods, which demonstrates the great effectiveness of the DGKs for image-set classification.