The precise diagnosis of Alzheimer's disease is critical for patient treatment, especially at the early stage, because awareness of the severity and progression risks lets patients take preventative actions before irreversible brain damage occurs. It is possible to gain a holistic view of Alzheimer's disease staging by combining multiple data modalities, known as image fusion. In this paper, the study proposes the early detection of Alzheimer's disease using different modalities of Alzheimer's disease brain images. First, the preprocessing was performed on the data. Then, the data augmentation techniques are used to handle overfitting. Also, the skull is removed to lead to good classification. In the second phase, two fusion stages are used: pixel level (early fusion) and feature level (late fusion). We fused magnetic resonance imaging and positron emission tomography images using early fusion (Laplacian Re-Decomposition) and late fusion (Canonical Correlation Analysis). The proposed system used magnetic resonance imaging and positron emission tomography to take advantage of each. Magnetic resonance imaging system's primary benefits are providing images with excellent spatial resolution and structural information for specific organs. Positron emission tomography images can provide functional information and the metabolisms of particular tissues. This characteristic helps clinicians detect diseases and tumor progression at an early stage. Third, the feature extraction of fused images is extracted using a convolutional neural network. In the case of late fusion, the features are extracted first and then fused. Finally, the proposed system performs XGB to classify Alzheimer's disease. The system's performance was evaluated using accuracy, specificity, and sensitivity. All medical data were retrieved in the 2D format of 256 × 256 pixels. The classifiers were optimized to achieve the final results: for the decision tree, the maximum depth of a tree was 2. The best number of trees for the random forest was 60; for the support vector machine, the maximum depth was 4, and the kernel gamma was 0.01. The system achieved an accuracy of 98.06%, specificity of 94.32%, and sensitivity of 97.02% in the case of early fusion. Also, if the system achieved late fusion, accuracy was 99.22%, specificity was 96.54%, and sensitivity was 99.54%.