In this paper, we propose a new feature selection method to exploit the issue of High Dimension Low Sample Size (HDLSS) for the prediction of Mild Cognitive Impairment (MCI) conversion. Specially, by regarding the Magnetic Resonance Imaging (MRI) information of MCI subjects as the target data, this paper proposes to integrate auxiliary information with the target data in a unified feature selection framework for distinguishing progressive MCI (pMCI) subjects from stable MCI (sMCI) subjects, i.e., the MCI conversion classification for short in this paper, based on their MRI information. The auxiliary information includes the Positron Emission Tomography (PET) information of the target data, the MRI information of Alzheimer’s Disease (AD) subjects and Normal Control (NC) subjects, and the ages of the target data and the AD and NC subjects. As a result, the proposed method jointly selects features from the auxiliary data and the target data by taking into account the influence of outliers and aging of these two kinds of data. Experimental results on the public data of Alzheimer’s Disease Neuroimaging Initiative (ADNI) verified the effectiveness of our proposed method, compared to three state-of-the-art feature selection methods, in terms of four classification evaluation metrics.