Feature selection has been widely used in machine learning for a long time. In this paper, we propose a supervised local sparse discriminative feature selection method named LSDFS to obtain sparse features by imposing ℓ 2, 0-norm constraint on transformation matrix. Differently from traditional approaches, our method does not require approximation or relaxation schemes, such as ℓ 2, p-norm to solve long-standing challenge. Our method is based on the trace difference form of Linear Discriminant Analysis (LDA), which can efficiently obtain discriminative information in low-dimensional space. In order to explore the local structure of data which contains more discriminative information, we adopt a sparse connections graph between anchor points and data points instead of fully-connected graph with time-consuming, and add a decay parameter to avoid trivial solutions, making the model more precisely. Extensive experiments conducted on synthetic datasets and several real-world datasets have demonstrated the advantages of our method.