The cortical atrophy measured from the magnetic resonance imaging (MRI) data along with aberrant neuronal activation patterns from the functional MRI data have been implicated in the mild cognitive impairment (MCI), which is a potential early form of a dementia. The association between the level of cortical atrophy in the gray matter (GM) and corresponding degree of neuronal connectivity, however, has not systematically been presented. In this study, we aimed to provide anecdotal evidence that there would be a close link between the anatomical abnormality and corresponding functional aberrance associated with the neuropsychiatric condition (i.e. MCI). Firstly, the voxel-based morphometry (VBM) analysis identified the medial temporal lobe and inferior parietal lobule as the regions with substantially decreased (i.e. atrophy) and increased GM concentrations, respectively. In the subsequent functional connectivity (FC) analysis via Pearson's correlation coefficients, the FC patterns using the regions with a decreased GM concentration showed increased FC patterns (i.e. hyper-connectivity) associated with the MCI. On the other hand, the FC patterns using the seed regions with an increased GM concentration have shown decreased FC (i.e. hypo-connectivity) with the MCI in the task anti-correlated regions including superior frontal gyrus (i.e. task-negative networks or default-mode networks). These results provide a supplemental information that there may be an compensatory mechanism in the human brain function, which potentially allow to diagnose early phase of the neuropsychiatric illnesses including the Alzheimer's diseases (AD).