Alzheimer disease is a form of dementia that results in memory-related problems in human beings. An accurate detection and classification of Alzheimer disease and its stages plays a crucial role in human health monitoring system. In this research paper, Alzheimer disease classification was assessed by Alzheimer's disease Neuro-Imaging Initiative (ADNI) dataset. After performing histogram equalization and skull removal of the collected brain images, segmentation was carried-out using Fuzzy C-Means (FCM) for segmenting the white matter, Cerebro-Spinal Fluid (CSF), and grey matter from the pre-processed brain images. Then, hybrid feature extraction (Histogram of Oriented Gradients (HOG), Local Binary Patterns (LBP), and Gray-Level Co-Occurrence Matrix (GLCM)) was performed for extracting the feature values from the segmented brain images. After hybrid feature extraction, reliefF feature selection was used for selecting the optimal feature subsets or to reject the irrelevant feature vectors. Then, the selected optimal feature vectors were given as the input to a supervised classifier Support Vector Machine (SVM) to classify three Alzheimer classes of subjects; those are normal, Alzheimer disease and Mild Cognitive Impairment (MCI). The experimental outcome showed that the proposed methodology performed effectively by means of sensitivity, accuracy, specificity, and f-score. The proposed methodology enhanced the classification accuracy up to 2-20% compared to the existing methodologies.