Previous studies have demonstrated that the accumulation of amyloid-β (Aβ) pathologies has distinctive stage-specific effects on the structural and functional brain networks along the Alzheimer’s disease (AD) continuum. A more comprehensive account of both types of brain network may provide a better characterization of the stage-specific effects of Aβ pathologies. A potential candidate for this joint characterization is the coupling between the structural and functional brain networks (SC-FC coupling). We therefore investigated the effect of Aβ accumulation on global SC-FC coupling in patients with mild cognitive impairment (MCI), AD, and healthy controls. Patients with MCI were dichotomized according to their level of Aβ pathology seen in 18F-flutemetamol PET-CT scans—namely, Aβ-negative and Aβ-positive. Our results show that there was no difference in global SC-FC coupling between different cohorts. During the prodromal AD stage, there was a significant negative correlation between the level of Aβ pathology and the global SC-FC coupling of MCI patients with positive Aβ, but no significant correlation for MCI patients with negative Aβ. During the AD dementia stage, the correlation between Aβ pathology and global SC-FC coupling in patients with AD was positive. Our results suggest that Aβ pathology has distinctive stage-specific effects on global coupling between the structural and functional brain networks along the AD continuum.