Hyperspectral image (HSI) contains a large number of spatial-spectral information, which will make the traditional classification methods face an enormous challenge to discriminate the types of land-cover. Feature learning is very effective to improve the classification performances. However, the current feature learning approaches are mostly based on a simple intrinsic structure. To represent the complex intrinsic spatial-spectral of HSI, a novel feature learning algorithm, termed spatial-spectral hypergraph discriminant analysis (SSHGDA), has been proposed on the basis of spatial-spectral information, discriminant information, and hypergraph learning. SSHGDA constructs a reconstruction between-class scatter matrix, a weighted within-class scatter matrix, an intraclass spatial-spectral hypergraph, and an interclass spatial-spectral hypergraph to represent the intrinsic properties of HSI. Then, in low-dimensional space, a feature learning model is designed to compact the intraclass information and separate the interclass information. With this model, an optimal projection matrix can be obtained to extract the spatial-spectral features of HSI. SSHGDA can effectively reveal the complex spatial-spectral structures of HSI and enhance the discriminating power of features for land-cover classification. Experimental results on the Indian Pines and PaviaU HSI data sets show that SSHGDA can achieve better classification accuracies in comparison with some state-of-the-art methods.