Speech comprehension in noisy environments depends on central auditory functions, which are vulnerable in Alzheimer's disease (AD). Binaural processing exploits two ear sounds to optimally process degraded sound information; its characteristics are poorly understood in AD. We studied behavioral and electrophysiological alterations in binaural processing among 121 participants (AD = 27; amnestic mild cognitive impairment [aMCI] = 33; subjective cognitive decline [SCD] = 30; cognitively normal [CN] = 31). We observed impairment of binaural processing in AD and aMCI, and detected a U-shaped curve change in phase synchrony (declining from CN to SCD and to aMCI, but increasing from aMCI to AD). This improvement in phase synchrony accompanying more severe cognitive stages could reflect neural adaptation for binaural processing. Moreover, increased phase synchrony is associated with worse memory during the stages when neural adaptation apparently occurs. These findings support a hypothesis that neural adaptation for binaural processing deficit may exacerbate cognitive impairment, which could help identify biomarkers and therapeutic targets in AD.