Classical linear regression not only lacks of the flexibility in fitting the label, but also ignores to preserve the intrinsic local geometric structure of data, which leads to overfitting. In this paper, we propose a novel discriminative regression method, called adaptive locality preserving based discriminative regression (ALPDR), to address these problems. Firstly, a locality preserving constraint regularized by the adaptive weight is introduced to preserve the intrinsic geometric structures of data, in which the similar points of the same class are adaptively pulled together by the projection. Secondly, ALPDR directly learns the discriminative target matrix from data based on the given label information, which allows more freedom in label fitting and simultaneously enlarges the margins between different classes. Thirdly, ALPDR imposes a row-sparsity constraint on the projection, which enables the method to adaptively select the most discriminative features from data such that the negative influence of noises and redundant features can be eliminated. Finally, an efficient iterative algorithm is provided to optimize the model. Extensive experiments show that the proposed method outperforms the other state-of-art methods, which proves the effectiveness of the proposed method.