Alzheimer's Disease (AD) is a progressive neurodegenerative disorder and the most commonly diagnosed cause of dementia, and it is the fifth leading cause of death among people aged 65 and older. During the years, the early diagnosis of AD patients has been a significant concern for researchers, in view of the fact that early diagnosis not only can lead to saving lives of the AD patients but also could bring a considerable amount of saving in health and long-term care expenditures for both people and the government. Mild cognitive impairment (MCI), defined as a transitional state between being healthy and having AD, is considered an established risk factor for AD. Hence, an accurate and reliable diagnosis of MCI and, consequently, discrimination between healthy people, MCI individuals, and AD patients can play a crucial role in the early diagnosis of AD. In recent years, analysis of blood gene expression data has been grabbed more attention than the conventional AD diagnosis method because it provides the opportunity to investigate the biochemical pathways, cellular functions, and regulatory mechanisms for finding the key genes associated with MCI and AD. Therefore, in this study, we employed blood gene expression data from Alzheimer's Disease Neuroimaging Initiative (ADNI), two feature selection methods for determining the most prominent genes related to MCI and AD, and three classifiers for the most accurate discrimination between three groups of healthy, MCI and AD. The proposed method yielded the selection of top ten genes from more than 49,000 genes and the best overall classification result between healthy and AD patients with average values of the area under the curve (AUC) of 0.77 +- 0.08. Furthermore, gene ontology (GO) analysis revealed that four genes were enriched with the GO terms of regulation of cell proliferation, negative regulation of cell population proliferation, signaling receptor binding, biological adhesion, and cytokine production.