Accurate representation of the Atlantic Meridional Overturning Circulation (AMOC) in global climate models is crucial for reliable future climate predictions and projections. In this study, we used 42 coupled atmosphere–ocean global climate models to analyze low-frequency variability of the AMOC driven by the North Atlantic Oscillation (NAO). Our results showed that the influence of the simulated NAO on the AMOC differs significantly between the models. We showed that the large intermodel diversity originates from the diverse oceanic mean state, especially over the subpolar North Atlantic (SPNA), where deep water formation of the AMOC occurs. For some models, the climatological sea ice extent covers a wide area of the SPNA and restrains efficient air–sea interactions, making the AMOC less sensitive to the NAO. In the models without the sea-ice-covered SPNA, the upper-ocean mean stratification critically affects the relationship between the NAO and AMOC by regulating the AMOC sensitivity to surface buoyancy forcing. Our results pinpoint the oceanic mean state as an aspect of climate model simulations that must be improved for an accurate understanding of the AMOC.