Alzheimer‘s disease (AD) is a neurodegenerative disease which is progressive and can be described by amyloid deposition, and neuronal atrophy. In this study, a support vector machine (SVM) approach with radial basis function (RBF) has been proposed in order to detect the Alzheimer's disease in its early stage using multiple modalities, including positron emission tomography (PET), magnetic resonance imaging (MRI), and standard neuropsychological test scores. A total number of 896 participants from the Alzheimer's Disease Neuroimaging Initiative (ADNI) were considered in this study. The proposed approach is able to classify cognitively normal control (CN) group from early mild cognitive impairment (EMCI) with an accuracy of 81.1%. In addition, the accuracy of 91.9% for CN vs. late mild cognitive impairment and accuracy of 96.2% for CN vs. AD classifications have been achieved through the proposed model.