Early diagnosis of Alzheimer’s disease (AD) allows individuals and their health managers to manage healthier medication. We proposed an approach for classification of AD stages, with respect to principal component analysis (PCA)-based algorithm. The PCA has been extensively applied as the most auspicious face-recognition algorithm. For the proposed algorithm, 100 images of 10 children were transformed for feature extraction and covariance matrix was constructed to obtain eigenvalues. The eigenvector provided a useful framework for face recognition. For the classification of AD stages, magnetic resonance imaging (MRI) and functional magnetic resonance imaging (fMRI) data were obtained from Alzheimer’s Disease Neuroimaging Initiative database. Hippocampus is one of the most affected regions by AD. Thus, we selected clusters of voxels from the “hippocampus” of AD screening stage (mild cognitive impairment), AD stage 1, AD stage 2, and AD stage 3. By using eigenvectors corresponding to maximum eigenvalues of fMRI data, the purposed algorithm classified the voxels of AD stages effectively.