Linear discriminant analysis (LDA) is one of the most popular methods for dimensionality reduction, and there have many different variants based on LDA. However, conventional LDA have some drawbacks: 1) The projection matrix offers the disadvantage of interpretability; 2) LDA assumes that every class data are drawn from Gaussian distribution which may not be applicable to many real-world data. Aiming to solve these problems, we propose a robust feature selection method, namely Self-weighted Locality Discriminative Feature Selection (SLD-FS), by combining row sparsity l2,1-norm regularization and self-weighted locality discriminant analysis strategy. Additionally, an effective iterative algorithm is developed to optimise this objective function, and the algorithm is proved to convergence. Extensive experiments conducted on various data sets demonstrate the effectiveness of SLD-FS when compared with some state-of-the-art supervised feature selection methods.