Alzheimer’s Disease (AD) poses a significant health risk globally, particularly among the elderly population. Recent studies underscore its prevalence, with over 50% of elderly Japanese facing a lifetime risk of dementia, primarily attributed to AD. As the most prevalent form of dementia, AD gradually erodes brain cells, leading to severe neurological decline. In this scenario, it is important to develop an automatic AD-detection system, and many researchers have been working to develop an AD-detection system by taking advantage of the advancement of deep learning (DL) techniques, which have shown promising results in various domains, including medical image analysis. However, existing approaches for AD detection often suffer from limited performance due to the complexities associated with training hierarchical convolutional neural networks (CNNs). In this paper, we introduce a novel multi-stage deep neural network architecture based on residual functions to address the limitations of existing AD-detection approaches. Inspired by the success of residual networks (ResNets) in image-classification tasks, our proposed system comprises five stages, each explicitly formulated to enhance feature effectiveness while maintaining model depth. Following feature extraction, a deep learning-based feature-selection module is applied to mitigate overfitting, incorporating batch normalization, dropout and fully connected layers. Subsequently, machine learning (ML)-based classification algorithms, including Support Vector Machines (SVM), Random Forest (RF) and SoftMax, are employed for classification tasks. Comprehensive evaluations conducted on three benchmark datasets, namely ADNI1: Complete 1Yr 1.5T, MIRAID and OASIS Kaggle, demonstrate the efficacy of our proposed model. Impressively, our model achieves accuracy rates of 99.47%, 99.10% and 99.70% for ADNI1: Complete 1Yr 1.5T, MIRAID and OASIS datasets, respectively, outperforming existing systems in binary class problems. Our proposed model represents a significant advancement in the AD-analysis domain.