Random Forest (RF) is a bagging ensemble model and has many important advantages, such as robustness to noise, an effective structure for complex multimodal data and parallel computing, and also provides important features that help investigate biomarkers. Despite these benefits, RF is not used actively to predict Alzheimer’s disease (AD) with brain MRIs. Recent studies have reported RF’s effectiveness in predicting AD, but the test sample sizes were too small to draw any solid conclusions. Thus, it is timely to compare RF with other learning model methods, including deep learning, particularly with large amounts of data. In this study, we tested RF and various machine learning models with regional volumes from 2250 brain MRIs: 687 normal controls (NC), 1094 mild cognitive impairment (MCI), and 469 AD that ADNI (Alzheimer’s Disease Neuroimaging Initiative database) provided. Three types of features sets (63, 29, and 22 features) were selected, and classification accuracies were computed with RF, Support vector machine (SVM), Multi-layer perceptron (MLP), and Convolutional neural network (CNN). As a result, RF, MLP, and CNN showed high performances of 90.2%, 89.6%, and 90.5% with 63 features. Interestingly, when 22 features were used, RF showed the smallest decrease in accuracy, −3.8%, and the standard deviation did not change significantly, while MLP and CNN yielded decreases in accuracy of −6.8% and −4.5% with changes in the standard deviation from 3.3% to 4.0% for MLP and 2.1% to 7.0% for CNN, indicating that RF predicts AD more reliably with fewer features. In addition, we investigated the importance of the features that RF provides, and identified the hippocampus, amygdala, and inferior lateral ventricle as the major contributors in classifying NC, MCI, and AD. On average, AD showed smaller hippocampus and amygdala volumes and a larger volume of inferior lateral ventricle than those of MCI and NC.