Alzheimer’s disease (AD) is a progressive neurological problem that causes brain atrophy and affects the memory and thinking skills of an individual. Accurate detection of AD has been a challenging research topic for a long time in the area of medical image processing. Detecting AD at its earliest stage is crucial for the successful treatment of the disease. The proposed Adaptive Hybrid Attention Network (AHANet) has two attention modules, namely Enhanced Non-Local Attention (ENLA) and Coordinate Attention. These modules extract global-level features and local-level features separately from the brain Magnetic Resonance Imaging (MRI), thereby boosting the feature extraction power of the network. The ENLA module extracts spatial and contextual information on a global scale while also capturing important long-range dependencies. The Coordinate Attention module captures local features from the input images. It embeds positional information into the channel attention mechanism for enhanced feature extraction. Moreover, an Adaptive Feature Aggregation (AFA) module is proposed to fuse features from the global and local levels in an effective way. As a result of incorporating the above architectural enhancements into the DenseNet architecture, the proposed network exhibited better performance compared to the existing works. The proposed network was trained and tested on the ADNI dataset, yielding a classification accuracy of 98.53%.