FluoroDeoxyGlucose Positron Emission Tomography (FDG- PET) is an important and effective modality used for diagnosing Alzheimer's Disease (AD) or Mild Cognitive Impairment (MCI). In this paper, we develop a novel method by using single modality (FDG- PET) but multi-level features, which considers both region properties and connectivities between regions, to diagnose AD or MCI. First, post-processed FDG-PET images are segmented into 116 Regions of Interest according to Automated Anatomical Labeling atlas. Second, three levels of features are extracted. Then the 2nd-Level feature is decomposed into 3 different sets of features according to a proposed similarity-driven ranking method, which can not only reduce the feature dimension but also increase the classifier's diversity. Last, after feeding the 3 levels of features to different classifiers, the majority voting, is applied to make the prediction. Experiments on ADNI database show that the proposed method outperforms other FDG-PET-based classification algorithms.