Alzheimer’s disease (AD) is characterized by the gradual deterioration of brain structures and changes in hemispheric asymmetry. Meanwhile, healthy aging is associated with a decrease in functional hemispheric asymmetry. In this study, functional connectivity analysis was used to compare the functional hemispheric asymmetry in eyes-open resting-state fNIRS data of 16 healthy elderly controls (mean age: 60.4 years, MMSE (Mini-Mental State Examination): 27.3 ± 2.52) and 14 Alzheimer’s patients (mean age: 73.8 years, MMSE: 22 ± 4.32). Increased interhemispheric functional connectivity was found in the premotor cortex, supplementary motor cortex, primary motor cortex, inferior parietal cortex, primary somatosensory cortex, and supramarginal gyrus in the control group compared to the AD group. The study revealed that the control group had stronger interhemispheric connectivity, leading to a more significant decrease in hemispheric asymmetry than the AD group. The results show that there is a difference in interhemispheric functional connections at rest between the Alzheimer’s group and the control group, suggesting that functional hemispheric asymmetry continues in Alzheimer’s patients.