Alzheimer's disease (AD) is a neurodegenerative condition that has no definitive treatment and its early diagnosis can help to prevent or slow down its progress. Neuroimaging in particular, structural magnetic resonance imaging (sMRI) and the progress of artificial intelligence (AI) have significant attention in AD detection. In this study, 398 participants were used from the ADNI and OASIS global database of sMRI including 98 individuals with AD, 102 with early mild cognitive impairment (EMCI), 98 with late mild cognitive impairment (LMCI), and 100 normal controls (NC). The proposed model achieved high area under the curve (AUC) values and an accuracy of 99.7%, which is very remarkable for all four classes: NC vs. AD: AUC = [0.985], EMCI vs. NC: AUC = [0.961], LMCI vs. NC: AUC = [0.951], LMCI vs. AD: AUC = [0.989], and EMCI vs. LMCI: AUC = [1.000]. The results reveal that this model incorporates DenseNet169, transfer learning, and class decomposition to classify AD stages, particularly in differentiating EMCI from LMCI. Overall, this model performs well with high accuracy and area under the curve for AD diagnostics at early stages.