Communication within the brain is highly dynamic. Alzheimer's disease (AD) exhibits dynamic progression corresponding to a decline in memory and cognition. However, little is known of whether brain dynamics are disrupted in AD and its prodromal stage, mild cognitive impairment (MCI). For our study, we acquired high sampling rate functional near-infrared spectroscopy imaging data at rest from the entire cortex of 23 patients with AD dementia, 25 patients with amnestic mild cognitive impairment (aMCI), and 30 age-matched healthy controls (HCs). Sliding-window correlation and k-means clustering analyses were used to construct dynamic functional connectivity (FC) maps for each participant. We discovered that the brain's dynamic FC variability strength (Q) significantly increased in both aMCI and AD group as compared to HCs. Using the Q value as a measurement, the classification performance exhibited a good power in differentiating aMCI [area under the curve (AUC = 82.5%)] or AD (AUC = 86.4%) from HCs. Furthermore, we identified two abnormal brain FC states in the AD group, of which the occurrence frequency (F) exhibited a significant decrease for the first-level FC state (state 1) and a significant increase for the second-level FC state (state 2). We also found that the abnormal F in these two states significantly correlated with the cognitive impairment in patients. These findings provide the first evidence to demonstrate the disruptions of dynamic brain connectivity in aMCI and AD and extend the traditional static (i.e., time-averaged) FC findings in the disease (i.e., disconnection syndrome) and thus provide insights into understanding the pathophysiological mechanisms occurring in aMCI and AD.