Mixture of regressors (MoR) is a widely used regression approach for approximating nonlinear mappings between input and target outputs. However, existing learning procedures for MoR are prone to overfitting when only limited amounts of training data are available. To address this problem, we propose a new mixture regression model, named mixture of grouped regressors (MoGR). It partitions the individual regressors in the model into a set of groups, where the parameters of the regressors within each group are encouraged to take on similar values. As the parameters for each local regressor are learned using all data within a group, they tend to be better conditioned and more robust to noise in the training data. Extensive experiments on real-world head pose and gaze data demonstrate the benefits of our proposed MoGR model.