Linear Discriminant Analysis (LDA) has been widely used in supervised dimensionality reduction fields. However, LDA is usually weak in tackling data with Non-Gaussian distribution due to its incapability of extracting the intrinsic structure of data. In order to learn the intrinsic information more effectively, some dimensionality reduction methods incorporate the adaptive full-connected graph into the algorithm frame, but the defect is that the calculation of each pairwise distance is very time-consuming. In this letter, we propose a novel fast adaptive local subspace learning with regressive regularization model to solve the supervised dimensional reduction problem. Firstly, the adaptive anchor point graph is used to capture local structure information, which can greatly reduce computation complexity. Secondly, by using regressive regularization, the samples from different classes can be better separated in the projected space and the workload of selecting the optimal reduced dimension is easier. Moreover, entropy regularization is used to derive more appropriate weights. Finally, extensive experiments are conducted on real world data sets to verify the superiority of our model.