In this brief, we propose a new groupwise retargeted least squares regression (GReLSR) model for multicategory classification. The main motivation behind GReLSR is to utilize an additional regularization to restrict the translation values of ReLSR, so that they should be similar within same class. By analyzing the regression targets of ReLSR, we propose a new formulation of ReLSR, where the translation values are expressed explicitly. On the basis of the new formulation, discriminative least-squares regression can be regarded as a special case of ReLSR with zero translation values. Moreover, a groupwise constraint is added to ReLSR to form the new GReLSR model. Extensive experiments on various machine leaning data sets illustrate that our method outperforms the current state-of-the-art approaches.