The progression of Alzheimer's Disease (AD) has been proposed to comprise three stages, subjective cognitive decline (SCD), mild cognitive impairment (MCI), and AD. Was brain dynamics across the three stages smooth? Was there a critical transition? How could we characterize and study functional criticality of human brain? Based on dynamical characteristics of critical transition from nonlinear dynamics, we proposed a vertex-wise Index of Functional Criticality (vIFC) of fMRI time series in this study. Using 42 SCD, 67 amnestic MCI (aMCI), 34 AD patients as well as their age-, sex-, years of education-matched 54 NC, our new method vIFC successfully detected significant patient-normal differences for SCD and aMCI, as well as significant negative correlates of vIFC in the right middle temporal gyrus with total scores of Montreal Cognitive Assessment (MoCA) in SCD. In comparison, standard deviation of fMRI time series only detected significant differences between AD patients and normal controls. As an index of functional criticality of human brain derived from nonlinear dynamics, vIFC could serve as a sensitive neuroimaging marker for future studies; considering much more vIFC impairments in aMCI compared to SCD and AD, our study indicated aMCI as a critical stage across AD progression.