Sleep disturbances are one of the preventive factors to delay the onset and progression of Alzheimer's disease. Early identification of Alzheimer's disease patients prone to develop sleep disturbances to offer early medical intervention is important. Resting-state functional MRI is a widely used method to investigate the neural mechanisms and find neuroimaging biomarkers in neuropsychiatric diseases. In this study, we applied percent amplitude of fluctuation (PerAF) and mPerAF (divided by global mean PerAF) to test the strength of intrinsic brain activity in 38 mild Alzheimer's disease patients with sleep disturbances (ADSD) and 21 mild Alzheimer's disease patients without sleep disturbances (ADNSD). Compared with ADNSD, we found decreased intrinsic brain activity in the calcarine gyrus, the lingual gyrus, the fusiform gyrus extending to the parahippocampal gyrus, the precentral gyrus, the postcentral gyrus (all in the left hemisphere) and the left brainstem. Conclusively, ADSD exhibited reduced neural activity in specific brain regions related to the sensorimotor network and the visual network, which indicated the contribution of sleep disturbances to the progression of Alzheimer's disease. Especially, the ventral visual pathway to the hippocampus might serve for the memory impaired by sleep disturbances in Alzheimer's disease, and the brainstem might be critical in the initiation of sleep disturbances in Alzheimer's disease. These findings further elucidate the interactions between Alzheimer's disease and sleep disturbances and could help with the early recognition of Alzheimer's disease patients who tend to develop sleep disturbances.