As a basic part of the atmosphere, the stratosphere plays an important role in the tropospheric climate and weather systems, especially during the winter, when the stratosphere and troposphere have their strongest interactions. This study assesses the abilities of the Fifth Phase of the Coupled Model Intercomparison Project (CMIP5) and CMIP3 models to simulate the boreal winter stratospheric polar vortex. Analysis indicates that the models with well-resolved stratospheres, that is, with a high model top (HTOP) covering the whole stratosphere, a high vertical resolution (HVer) of the stratosphere, and nonorographic gravity wave drag (NOG), rank higher in both the temporal scoring system and the spatial scoring system. The extreme cold polar vortex bias, which was found in the CMIP3 models, vanishes in the CMIP5 models with HTOP, HVer, and NOG but persists in the other CMIP5 models. A dynamical analysis shows that the heat flux propagating into the stratosphere is stronger in models with HTOP, HVer, and NOG, but these propagations are still weaker than those in the ERA40 reanalysis, indicating the lack of variability in the current CMIP5 models.