Alzheimer’s disease (AD) is one of the most common neurodegenerative illnesses (dementia) among the elderly. Recently, researchers have developed a new method for the instinctive analysis of AD based on machine learning and its subfield, deep learning. Recent state-of-the-art techniques consider multimodal diagnosis, which has been shown to achieve high accuracy compared to a unimodal prognosis. Furthermore, many studies have used structural magnetic resonance imaging (MRI) to measure brain volumes and the volume of subregions, as well as to search for diffuse changes in white/gray matter in the brain. In this study, T1-weighted structural MRI was used for the early classification of AD. MRI results in high-intensity visible features, making preprocessing and segmentation easy. To use this image modality, we acquired four types of datasets from each dataset’s server. In this work, we downloaded 326 subjects from the National Research Center for Dementia homepage, 123 subjects from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) homepage, 121 subjects from the Alzheimer’s Disease Repository Without Borders homepage, and 131 subjects from the National Alzheimer’s Coordinating Center homepage. In our experiment, we used the multiatlas label propagation with expectation–maximization-based refinement segmentation method. We segmented the images into 138 anatomical morphometry images (in which 40 features belonged to subcortical volumes and the remaining 98 features belonged to cortical thickness). The entire dataset was split into a 70 : 30 (training and testing) ratio before classifying the data. A principal component analysis was used for dimensionality reduction. Then, the support vector machine radial basis function classifier was used for classification between two groups—AD versus health control (HC) and early mild cognitive impairment (MCI) (EMCI) versus late MCI (LMCI). The proposed method performed very well for all four types of dataset. For instance, for the AD versus HC group, the classifier achieved an area under curve (AUC) of more than 89% for each dataset. For the EMCI versus LMCI group, the classifier achieved an AUC of more than 80% for every dataset. Moreover, we also calculated Cohen kappa and Jaccard index statistical values for all datasets to evaluate the classification reliability. Finally, we compared our results with those of recently published state-of-the-art methods.