Recently, sparse graph-based discriminant analysis (SGDA) has been developed for the dimensionality reduction and classification of hyperspectral imagery. In SGDA, a graph is constructed by l(1)-norm optimization based on available labeled samples. Different from traditional methods (e.g., k-nearest neighbor with Euclidean distance), weights in an l(1)-graph derived via a sparse representation can automatically select more discriminative neighbors in the feature space. However, the sparsity-based graph represents each sample individually, lacking a global constraint on each specific solution. As a consequence, SGDA may be ineffective in capturing the global structures of data. To overcome this drawback, a sparse and low-rank graph-based discriminant analysis (SLGDA) is proposed. Low-rank representation has been proved to be capable of preserving global data structures, although it may result in a dense graph. In SLGDA, a more informative graph is constructed by combining both sparsity and low rankness to maintain global and local structures simultaneously. Experimental results on several different multiple-class hyperspectral-classification tasks demonstrate that the proposed SLGDA significantly outperforms the state-of-the-art SGDA.