Recently, multi-task based feature selection methods have been used in multi-modality based classification of Alzheimer's disease (AD) and its prodromal stage, i.e., Mild cognitive impairment (MCI). However, in traditional multi-task feature selection methods, some useful discriminative information among subjects is usually not well mined for further improving the subsequent classification performance. Accordingly, in this paper, we propose a discriminative multi-task feature selection method to select the most discriminative features for multi-modality based classification of AD/MCI. Specifically, for each modality, we traina linear regression model using the corresponding modality of data, and further enforce the group-sparsity regularization on weights of those regression models for joint selection of common features across multiple modalities. Furthermore, we propose a discriminative regularization term based on the intra-class and inter-class Laplacian matrices to better use the discriminative information among subjects. We perform extensive experiments on 202 subjects from the baseline MRI and FDG-PET image data of the Alzheimer's Disease Neuroimaging Initiative (ADNI). The experimental results show that our proposed method improves the classification performance with the comparison to several state-of the-art methods for multi-modality based AD/MCI classification.