Alzheimer's disease (AD) is a widespread neurodegenerative disease that causes 60–80% of all dementias and has a large economic impact in developed countries. For early‐stage AD detection, volumetric measures of magnetic resonance imaging (MRI) have proven to be a benchmark method. To detect potential cases, existing methods combine health records, neuropsychological testing, and MRI, although learning implementation is inconsistently used and has low sensitivity and specificity. Furthermore, numerous classification approaches for diagnosing AD have been suggested with differing complexity. Thus, we have introduced our novel AD diagnosis model with two main phases such as proposed feature extraction and classification. In the first phase, the gray‐level co‐occurrence matrix (GLCM), Haralick features as well as proposed geometric Haralick features known as geometric correlation and variance are extracted. In the second phase, an optimized deep convolutional neural network (DCNN) is utilized for classification. To make the prediction more accurate, the weight and the activation function of DCNN are optimally chosen by a new hybrid model termed as Combined Gray Wolf and Dragon Updating (CG‐DU). At last, the superiority of the adopted scheme is validated in terms of performance analysis, convergence analysis, box plot analysis, and computation time analysis. Especially, the proposed model achieves a mean accuracy of 0.98795, sensitivity of 0.98671, and specificity of 0.99429. Moreover, the computation time of the CG‐DU model is 2.92%, and 0.14% superior to existing GWO and DA methods respectively.