Linear discriminant analysis (LDA) is a very popular supervised feature extraction method and has been extended to different variants. However, classical LDA has the following problems: 1) The obtained discriminant projection does not have good interpretability for features; 2) LDA is sensitive to noise; and 3) LDA is sensitive to the selection of number of projection directions. In this paper, a novel feature extraction method called robust sparse linear discriminant analysis (RSLDA) is proposed to solve the above problems. Specifically, RSLDA adaptively selects the most discriminative features for discriminant analysis by introducing the <inline-formula> <tex-math notation="LaTeX">l_{2,1} </tex-math></inline-formula> norm. An orthogonal matrix and a sparse matrix are also simultaneously introduced to guarantee that the extracted features can hold the main energy of the original data and enhance the robustness to noise, and thus RSLDA has the potential to perform better than other discriminant methods. Extensive experiments on six databases demonstrate that the proposed method achieves the competitive performance compared with other state-of-the-art feature extraction methods. Moreover, the proposed method is robust to the noisy data.