In this article, we propose a new linear regression (LR)-based multiclass classification method, called discriminative regression with adaptive graph diffusion (DRAGD). Different from existing graph embedding-based LR methods, DRAGD introduces a new graph learning and embedding term, which explores the high-order structure information between four tuples, rather than conventional sample pairs to learn an intrinsic graph. Moreover, DRAGD provides a new way to simultaneously capture the local geometric structure and representation structure of data in one term. To enhance the discriminability of the transformation matrix, a retargeted learning approach is introduced. As a result of combining the above-mentioned techniques, DRAGD can flexibly explore more unsupervised information underlying the data and the label information to obtain the most discriminative transformation matrix for multiclass classification tasks. Experimental results on six well-known real-world databases and a synthetic database demonstrate that DRAGD is superior to the state-of-the-art LR methods.