Convolutional neural networks (CNNs) have been increasingly used in the computer-aided diagnosis of Alzheimer’s Disease (AD). This study takes the advantage of the 2D-slice CNN fast computation and ensemble approaches to develop a Monte Carlo Ensemble Neural Network (MCENN) by introducing Monte Carlo sampling and an ensemble neural network in the integration with ResNet50. Our goals are to improve the 2D-slice CNN performance and to design the MCENN model insensitive to image resolution. Unlike traditional ensemble approaches with multiple base learners, our MCENN model incorporates one neural network learner and generates a large number of possible classification decisions via Monte Carlo sampling of feature importance within the combined slices. This can overcome the main weakness of the lack of 3D brain anatomical information in 2D-slice CNNs and develop a neural network to learn the 3D relevance of the features across multiple slices. Brain images from Alzheimer’s Disease Neuroimaging Initiative (ADNI, 7199 scans), the Open Access Series of Imaging Studies-3 (OASIS-3, 1992 scans), and a clinical sample (239 scans) are used to evaluate the performance of the MCENN model for the classification of cognitively normal (CN), patients with mild cognitive impairment (MCI) and AD. Our MCENN with a small number of slices and minimal image processing (rigid transformation, intensity normalization, skull stripping) achieves the AD classification accuracy of 90%, better than existing 2D-slice CNNs (accuracy: 63%∼84%) and 3D CNNs (accuracy: 74%∼88%). Furthermore, the MCENN is robust to be trained in the ADNI dataset and applied to the OASIS-3 dataset and the clinical sample. Our experiments show that the AD classification accuracy of the MCENN model is comparable when using high- and low-resolution brain images, suggesting the insensitivity of the MCENN to image resolution. Hence, the MCENN does not require high-resolution 3D brain structural images and comprehensive image processing, which supports its potential use in a clinical setting.