This study introduces a novel Gaussian discriminant analysis (GDA)-based computer aided diagnosis (CAD) system using structural magnetic resonance imaging (MRI) data uniquely as input for screening different stages of Alzheimers disease (AD) involving its prodromal stage of mild cognitive impairment (MCI) in relation to the cognitive normal control group (CN). Taking advantage of multiple modalities of biomarkers, over the past few years, several machine learning-based CAD approaches have been proposed to address this high-dimensional classification problem. This study presents a novel GDA-based CAD system on the basis of a tenfold cross validation and a held-out test data set. Subjects considered in this study included 187 CN, 301 MCI, and 131 AD subjects from the Alzheimers Disease Neuroimaging Initiative (ADNI) database. In the tenfold cross validation, the proposed system achieved an average F1 score of 97.20%, accuracy of 96.00%, sensitivity of 99.14%, and specificity of 88.67% for discriminating together the MCI and AD groups from the CN group; and an average F1 score of 79.82%, accuracy of 87.43%, sensitivity of 79.09%, and specificity of 91.25% for discriminating AD from MCI. By testing on the held-out test data, for discriminating MCI and AD from CN, an accuracy of 93.28%, a sensitivity of 98.78%, and a specificity of 81.08% were obtained. These results also show that by separating left and right hemispheres of the brain into two decisional spaces, and then combining their outputs, the GDA-based CAD system demonstrates a high potential for clinical application.