Alzheimer’s disease (AD) is a neurodegenerative disease that affects brain cells, and mild cognitive impairment (MCI) has been defined as the early phase that describes the onset of AD. Early detection of MCI can be used to save patient brain cells from further damage and direct additional medical treatment to prevent its progression. Lately, the use of deep learning for the early identification of AD has generated a lot of interest. However, one of the limitations of such algorithms is their inability to identify changes in the functional connectivity in the functional brain network of patients with MCI. In this paper, we attempt to elucidate this issue with randomized concatenated deep features obtained from two pre-trained models, which simultaneously learn deep features from brain functional networks from magnetic resonance imaging (MRI) images. We experimented with ResNet18 and DenseNet201 to perform the task of AD multiclass classification. A gradient class activation map was used to mark the discriminating region of the image for the proposed model prediction. Accuracy, precision, and recall were used to assess the performance of the proposed system. The experimental analysis showed that the proposed model was able to achieve 98.86% accuracy, 98.94% precision, and 98.89% recall in multiclass classification. The findings indicate that advanced deep learning with MRI images can be used to classify and predict neurodegenerative brain diseases such as AD.