Observations show that there were warming trends in the stratospheric Arctic in early winter (November－December) since the late 1970s. To test whether the warming trends result from rising Sea Surface Temperature (SST), an atmospheric general circulation model (AGCM) is forced using observed global time-varying SST and sea ice concentrations. Ensemble simulations demonstrate that there are indeed statistically significant warming trends in the stratospheric Arctic under the SST forcing. The tropospheric Arctic also shows relatively weak warming trends, with lower statistical significance. Application of empirical orthogonal function (EOF) analysis to simulated geopotential heights reveals that the leading EOF modes of geopotential heights has a spatial pattern similar to that of the Arctic Oscillation (AO) or the Northern Hemisphere annular mode (NAM). In the stratosphere, the time series of the principal component shows a significant negative trend. Corresponding to the negative AO trend, wave activity at middle and high latitudes is increased, and zonal-mean zonal winds are decelerated, suggesting that the warming trends in the stratospheric Arctic are due to enhanced adiabatic heating in the Arctic stratosphere because of increased wave activity. In addition, simulations also show relatively weak warming trends in the Arctic lower stratosphere in late winter (February－March). Since increases in polar stratospheric temperatures tend to slow down heterogeneous ozone chemical reactions, the stratospheric Arctic warming will benefit ozone recovery.