In this paper, an efficient feature extraction method, named local structure preserving discriminant analysis (LSPDA), is presented. LSPDA constructs the local scatter and the between-class scatter to characterize the sub- and multi-manifold information respectively. More specifically, the local structure is constructed according to a certain kind of similarity between data points which takes special consideration of both the local information and the class information based on a parameter-free neighborhood decision rule, and the between-class structure is constructed according to the importance degrees of the not-same-class points measured by a strictly monotonically decreasing function. After the local scatter and the between-class scatter have been characterized, the novel feature extraction criterion is derived via maximizing the difference between the between-class scatter and the local scatter. Experimental results on the Wine dataset, AR, FERET, CMU PIE, ORL and LFW face databases show the effectiveness of the proposed method.