In the clinical study of Alzheimer's Disease (AD) with neuroimaging data, it is challenging to identify the progressive Mild Cognitive Impairment (pMCI) subjects from the stableMCI (sMCI) subjects (i.e., the pMCI/sMCI classification) in an individual level because of small inter-group differences between two groups (i.e., pMCIs and sMCIs) as well as high intra-group variations within each group. Moreover, there are a very limited number of subjects available, which cannot guarantee to find informative and discriminative patterns for achieving high diagnostic accuracy. In this paper, we propose a novel sparse regression method to fuse the auxiliary data into the predictor data for the pMCI/sMCI classification, where the predictor data is structural Magnetic Resonance Imaging (MRI) information of both pMCI and sMCI subjects and the auxiliary data includes the ages of the subjects, the Positron Emission Tomography (PET) information of the predictor data, and the structural MRI information of AD and Normal Controls (NC). Specifically, we incorporate the auxiliary data and the predictor data into a unified framework to jointly achieve the following objectives: i) jointly selecting informative features from both the auxiliary data and the predictor data; ii) robust to outliers from both the auxiliary data and the predictor data; and iii) reducing the aging effect due to the possible cause of brain atrophy induced by both the normal aging and the disease progression. As a result, our proposed method jointly selects the useful features from the auxiliary data and the predictor data by taking into account the influence of outliers and the age of the two kinds of data, i.e., the pMCI and sMCI subjects as well as the AD and NC subjects. We further employ the linear Support Vector Machine (SVM) with the selected features of the predictor data to conduct the pMCI/sMCI classification. Experimental results on the public data of Alzheimer's Disease Neuroimaging Initiative (ADNI) show the proposed method achieved the best classification performance, compared to the best comparison method, in terms of four evaluation metrics.