Letter fluency task (LFT) is a tool that measures memory, executive function, and language function but lacks a definite cutoff value to define abnormalities. We used the optical signals of functional near-infrared spectroscopy (fNIRS) to study the differences in power and connectivity between the high-functioning and low-functioning participants while performing three successive LFTs, as well as the relationships between the brain network/power and LFT performance. We found that the most differentiating factor between these two groups was network topology rather than activation power. The high-functional group (7 men and 10 women) displayed higher left intra-hemispheric global efficiency, nodal strength, and shorter characteristic path length in the first section. They then demonstrated a higher power over the left Broca's area than the right corresponding area in the latter two sections. The low-LFT group (9 men and 11 women) displayed less left-lateralized connectivity and activation power. LFT performance was only related to the network topology rather than the power values, which was only presented in the low-functioning group in the second section. The direct correlation between power and connectivity primarily existed in the inter-hemispheric network, with the timing relationship also seeming to be present. In conclusion, the high-functioning group presented more prominent left-lateralized intra-hemispheric network connectivity and power activation, particularly in the Broca's area. The low-functioning group seemed to prefer using other networks, like the inter-hemispheric, rather than having a single focus on left intra-hemispheric connectivity. The network topology seemed to better reflect the LFT performance than did the power values.