Alzheimer's disease (AD) patients often suffer from sleep disturbances. Alterations in sleep, especially rapid eye movement sleep (REMS), can precede the onset of dementia. To accurately characterize the sleep impairments accompanying AD and their underlying mechanisms using animal models, it is crucial to use models in which brain areas are affected in a manner similar to that observed in the actual patients. Here, we focused on mice, in which expression levels and patterns of mutated amyloid precursor protein (APP) follow the endogenous patterns. We characterized the sleep architecture of male homozygous and heterozygous mice at two ages (six and 12 months). At six months, homozygous mice exhibited reduced REMS, which was further reduced at 12 months together with a slight reduction in non-REMS (NREMS). By contrast, heterozygous mice exhibited an overall normal sleep architecture. Homozygous mice also exhibited decreased electroencephalogram γ to δ power ratio during REMS from six months, resembling the electroencephalogram slowing phenomenon observed in preclinical or early stages of AD. In addition, homozygous mice showed learning and memory impairments in the trace fear conditioning (FC) at both ages, and task performance strongly correlated with REMS amount at 12 months. Finally, histologic analyses revealed that amyloid-β accumulation in the pontine tegmental area and ventral medulla followed a course similar to that of the REMS reduction. These findings support the notion that changes in REMS are an early marker of AD and provide a starting point to address the mechanism of sleep deficits in AD and the effects on cognition.