In this paper, we propose a novel feature selection method by jointly considering (1) 'task-specific' relations between response variables (e.g., clinical labels in this work) and neuroimaging features and (2) 'self-representation' relations among neuroimaging features in a sparse regression framework. Specifically, the task-specific relation is devised to learn the relative importance of features for representation of response variables by a linear combination of the input features in a supervised manner, while the self-representation relation is used to take into account the inherent information among neuroimaging features such that any feature can be represented by a weighted sum of the other features, regardless of the label information, in an unsupervised manner. By integrating these two different relations along with a group sparsity constraint, we formulate a new sparse linear regression model for class-discriminative feature selection. The selected features are used to train a support vector machine for classification. To validate the effectiveness of the proposed method, we conducted experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset; experimental results showed superiority of the proposed method over the state-of-the-art methods considered in this work.