Locality preserving projection （LPP） has been widely used in feature extraction. However， LPP does not use category information of data， and uses L2-norm for distance measurement， which is highly sensitive to outliers. We consider the weight matrix of LPP from a supervised perspective， and combine the method of low-rank regression to propose a new model to discover and extract features. By using L2,1-norm to constrain the loss function and the regression matrix， not only the sensitivity to outliers is reduced， but also the low-rank condition of the regression matrix is restricted. Then we propose a solution to the optimization problem. Finally， we apply the method to a series of face database and palmprint dataset to test performance， and the experimental results show that the proposed method is effective.