Traditional local feature extraction algorithms are difficult to determine neighborhood parameters， and they only consider the single structure information of the data， which ignore important information. To solve the above problems， a Local Discrimination and Global Sparse Preservation Projection Algorithm（LDGSPP） based on sparse representation and learning graph regularity is proposed. The algorithm firstly applies a learning-based graph regularizer to the sparse representation model. Then the improved sparse representation model is used to reveal the local linear structure of the sample data adaptively. The local discriminant model global integration algorithm is used to extract the discriminant information of the local linear structure. The new sparse graph constructed by the improved sparse representation model is used to reveal the global sparse structure of data. The local discriminant structure and the global sparse structure of the data are preserved in the low dimensional feature space. 1-nearest neighbors and support vector machine classifier are used to evaluate the experimental results. The experiments on PaviaU and Indian Pines show that LDGSPP achieves the best performance compared with the comparison algorithm. As global and local discriminant information is extracted， the ground object classification accuracy of hyperspectral images is effectively improved.