This paper reports a functional connectivity analysis at prefrontal cortex (PFC) during semantic verbal fluency task (SVFT) for three groups of elderly people, i.e., normal aging (NA), mild cognitive impairment (MCI) and mild Alzheimer's disease (AD). Functional Near Infrared Spectroscopy (fNIRS) was used to measure neuronal activities. A new software algorithm was developed to process fNIRS signals and to derive the parameters of functional connectivity. The synchronization of oxygenated hemoglobin signals from paired channels was evaluated using their temporal correlation. Results from 61 subjects of experiment show that a general decline in functional connectivity from NA (edge count =307) to AD (edge count =170), and the laterality between left and right PFC became insignificant mathrm p>0.01) at AD stage. Moreover, the NA group demonstrated a significantly higher clustering coefficient than the AD group mathrm p< 0.01), indicating the NA has higher regularity in brain network. Using semantic verbal fluency task, this work demonstrated fNIRS as a feasible measuring instrument to differentiate AD from NA based on functional connectivity, with clustering coefficient and laterality as suitable biomarkers. © 2018 IEEE.