This study examines brain functional connectivity in both cognitively normal seniors and patients with mild cognitive impairment (MCI) to elucidate prospective markers of MCI. A homemade four-channel functional near-infrared spectroscopy (fNIRS) system was employed to measure hemodynamic responses in the subjects' prefrontal cortex during a resting state, an oddball task, a 1-back task, and a verbal fluency task. Brain functional connectivity was calculated as the Pearson correlation coefficients between fNIRS channels. The results show that during the verbal fluency task, while the healthy control (HC) group presents a significantly stronger inter-hemispheric connectivity compared to intra-hemispheric connectivity, there is no difference between the inter- and intra-hemispheric connectivity in the MCI group. In addition, a comparison between the MCI and HC connectivity reveals that the MCI group has a statistically higher right and inter-hemispheric connectivity during the resting state, but a significantly lower left and inter-hemispheric connectivity during the verbal fluency test. These findings demonstrate the potential of fNIRS to study brain functional connectivity in neurodegenerative diseases.