Neuroimage measures from magnetic resonance (MR) imaging, such as cortical thickness, have been playing an increasingly important role in searching for biomarkers of Alzheimer's disease (AD). Recent studies show that, AD, mild cognitive impairment (MCI) and normal control (NC) can be distinguished with relatively high accuracy using the baseline cortical thickness. With the increasing availability of large longitudinal datasets, it also becomes possible to study the longitudinal changes of cortical thickness and their correlation with the development of pathology in AD. In this study, the longitudinal cortical thickness changes of 152 subjects from 4 clinical groups (AD, NC, Progressive-MCI and Stable-MCI) selected from Alzheimer's Disease Neuroimaging Initiative (ADNI) are measured by our recently developed 4 D (spatial+temporal) thickness measuring algorithm. It is found that the 4 clinical groups demonstrate very similar spatial distribution of grey matter (GM) loss on cortex. To fully utilize the longitudinal information and better discriminate the subjects from 4 groups, especially between Stable-MCI and Progressive-MCI, 3 different categories of features are extracted for each subject, i.e., (1) static cortical thickness measures computed from the baseline and endline, (2) cortex thinning dynamics, such as the thinning speed (mm/year) and the thinning ratio (endline/baseline), and (3) network features computed from the brain network constructed based on the correlation between the longitudinal thickness changes of different regions of interest (ROIs). By combining the complementary information provided by features from the 3 categories, 2 classifiers are trained to diagnose AD and to predict the conversion to AD in MCI subjects, respectively. In the leave-one-out cross-validation, the proposed method can distinguish AD patients from NC at an accuracy of 96.1%, and can detect 81.7% (AUC = 0.875) of the MCI converters 6 months ahead of their conversions to AD. Also, by analyzing the brain network built via longitudinal cortical thickness changes, a significant decrease (p < 0.02) of the network clustering coefficient (associated with the development of AD pathology) is found in the Progressive-MCI group, which indicates the degenerated wiring efficiency of the brain network due to AD. More interestingly, the decreasing of network clustering coefficient of the olfactory cortex region was also found in the AD patients, which suggests olfactory dysfunction. Although the smell identification test is not performed in ADNI, this finding is consistent with other AD-related olfactory studies.