Mild cognitive impairment (MCI) is an intermediate stage between normal aging and dementia. Researchers tend to discuss its early state (early MCI, eMCI) due to its high conversion rate of dementia and poor treatment effect in the middle and late stages. Currently, the research on the disease evolution of the brain functional networks of patients with MCI has gradually become a research hotspot. In this study, we compare the differences in dynamic functional connectivity among eMCI, late MCI (lMCI), and normal control (NC) groups, and their graph theory indicators reveal the integration and segregation of functional connectivity states. Firstly, dynamic functional network windows were constructed based on the sliding time window method, and then these window samples were clustered by k-means to extract the functional connectivity states. The differences in the three groups were compared by analyzing the graph theory indicators, such as the participation coefficient, module degree distribution, clustering coefficient, global efficiency, and local efficiency, which distinguish the functional connectivity states. The results reveal that the NC group has the strongest integration and segregation, followed by the eMCI group, and the lMCI group has the weakest integration and segregation. We conclude that with the aggravation of MCI, the integration and segregation of dynamic functional connectivity states tend to decline. The results also reflect that the lMCI group has significantly more brain functional connections in some states, such as IPL.L-MTG.R and DCG.R-SMG.L, than the eMCI group, while the lMCI group has significantly less OLF.L-SPG.L than the NC group.