Effective and accurate diagnosis of Alzheimer's disease (AD), as well as its prodromal stage (i.e., mild cognitive impairment (MCI)), has attracted more and more attention recently. So far, multiple biomarkers have been shown to be sensitive to the diagnosis of AD and MCI, i.e., structural MR imaging (MRI) for brain atrophy measurement, functional imaging (e.g., FDG-PET) for hypometabolism quantification, and cerebrospinal fluid (CSF) for quantification of specific proteins. However, most existing research focuses on only a single modality of biomarkers for diagnosis of AD and MCI, although recent studies have shown that different biomarkers may provide complementary information for the diagnosis of AD and MCI. In this paper, we propose to combine three modalities of biomarkers, i.e., MRI, FDG-PET, and CSF biomarkers, to discriminate between AD (or MCI) and healthy controls, using a kernel combination method. Specifically, ADNI baseline MRI, FDG-PET, and CSF data from 51 AD patients, 99 MCI patients (including 43 MCI converters who had converted to AD within 18 months and 56 MCI non-converters who had not converted to AD within 18 months), and 52 healthy controls are used for development and validation of our proposed multimodal classification method. In particular, for each MR or FDG-PET image, 93 volumetric features are extracted from the 93 regions of interest (ROIs), automatically labeled by an atlas warping algorithm. For CSF biomarkers, their original values are directly used as features. Then, a linear support vector machine (SVM) is adopted to evaluate the classification accuracy, using a 10-fold cross-validation. As a result, for classifying AD from healthy controls, we achieve a classification accuracy of 93.2% (with a sensitivity of 93% and a specificity of 93.3%) when combining all three modalities of biomarkers, and only 86.5% when using even the best individual modality of biomarkers. Similarly, for classifying MCI from healthy controls, we achieve a classification accuracy of 76.4% (with a sensitivity of 81.8% and a specificity of 66%) for our combined method, and only 72% even using the best individual modality of biomarkers. Further analysis on MCI sensitivity of our combined method indicates that 91.5% of MCI converters and 73.4% of MCI non-converters are correctly classified. Moreover, we also evaluate the classification performance when employing a feature selection method to select the most discriminative MR and FDG-PET features. Again, our combined method shows considerably better performance, compared to the case of using an individual modality of biomarkers.