Two 1000-year numerical experiments based on the IFA RAN global climate model, the first with completely interacting atmosphere and ocean and the second with a fixed climatic mean annual cycle of sea surface temperature, are analyzed. In both cases, a quasi-decadal cyclicity (QDC), but with substantially different amplitude-frequency characteristics, is detected for the North Atlantic Oscillation (NAO) in winter. Significant changes in the QDC regimes from one century to another are observed in the model. A comparison of the numerical results with empirical data and reconstructions reveal a fairly good agreement of the QDC amplitude and periods for winter NAO regimes in the model with completely interacting atmosphere and ocean for individual model subperiods on the order of a century. The model results suggest that interdecadal NAO variations of natural origin can be noticeably strengthened in the climate system without any influence of external, in particular, anthropogenic factors. In the case of a fixed annual cycle of SST, the QDC amplitudes are underestimated several times by the model, and no positive correlation is observed between the amplitudes and periods of the NAO QDC in contrast to the empirical data, reconstructions, and the model with completely interacting atmosphere and ocean.