Due to the characteristics of lacking training sample poin ts in hyperspectral data,an unsupervised feature selection method to reduce dimension for hyperspectral data is represented.This method can keep the discriminant ability and local geometric structure of original data at the same time.In order to keep the disc riminant ability, the method reconstructs the original data using the selected features.Through m inimizing the reconstruction error,feature selection problem is transformed into an optimizat ion problem. In order to keep the local geometric structure,neighbor graph is established an d transformed into regular term,which is added into the objective function.Iterative gradien t descent method is used to solve this optimization problem.The optimal feature subset is used in hyperspectral image classification task.Experiments on real data sets show that the new method can improve the accuracy of classification.