In recent years, several high-dimensional, accurate, and effective classification methods have been proposed for the automatic discrimination of the subject between Alzheimer’s disease (AD) or its prodromal phase {i.e., mild cognitive impairment (MCI)} and healthy control (HC) persons based on T1-weighted structural magnetic resonance imaging (sMRI). These methods emphasis only on using the individual feature from sMRI images for the classification of AD, MCI, and HC subjects and their achieved classification accuracy is low. However, latest multimodal studies have shown that combining multiple features from different sMRI analysis techniques can improve the classification accuracy for these types of subjects. In this paper, we propose a novel classification technique that precisely distinguishes individuals with AD, aAD (stable MCI, who had not converted to AD within a 36-month time period), and mAD (MCI caused by AD, who had converted to AD within a 36-month time period) from HC individuals. The proposed method combines three different features extracted from structural MR (sMR) images using voxel-based morphometry (VBM), hippocampal volume (HV), and cortical and subcortical segmented region techniques. Three classification experiments were performed (AD vs. HC, aAD vs. mAD, and HC vs. mAD) with 326 subjects (171 elderly controls and 81 AD, 35 aAD, and 39 mAD patients). For the development and validation of the proposed classification method, we acquired the sMR images from the dataset of the National Research Center for Dementia (NRCD). A five-fold cross-validation technique was applied to find the optimal hyperparameters for the classifier, and the classification performance was compared by using three well-known classifiers: K-nearest neighbor, support vector machine, and random forest. Overall, the proposed model with the SVM classifier achieved the best performance on the NRCD dataset. For the individual feature, the VBM technique provided the best results followed by the HV technique. However, the use of combined features improved the classification accuracy and predictive power for the early classification of AD compared to the use of individual features. The most stable and reliable classification results were achieved when combining all extracted features. Additionally, to analyze the efficiency of the proposed model, we used the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset to compare the classification performance of the proposed model with those of several state-of-the-art methods.