The combined influences of the westerly phase of the quasi-biennial oscillation (QBO-W) and solar maximum (S_max) conditions on the Northern Hemisphere extratropical winter circulation are investigated using reanalysis data and Center for Climate System Research/National Institute for Environmental Studies chemistry climate model (CCM) simulations. The composite analysis for the reanalysis data indicates strengthened polar vortex in December followed by weakened polar vortex in February-March for QBO-W during S_max (QBO-W/S_max) conditions. This relationship need not be specific to QBO-W/S_max conditions but may just require strengthened vortex in December, which is more likely under QBO-W/S_max. Both the reanalysis data and CCM simulations suggest that dynamical processes of planetary wave propagation and meridional circulation related to QBO-W around polar vortex in December are similar in character to those related to S_max; furthermore, both processes may work in concert to maintain stronger vortex during QBO-W/S_max. In the reanalysis data, the strengthened polar vortex in December is associated with the development of north-south dipole tropospheric anomaly in the Atlantic sector similar to the North Atlantic oscillation (NAO) during December-January. The structure of the north-south dipole anomaly has zonal wavenumber 1 (WN1) component, where the longitude of anomalous ridge overlaps with that of climatological ridge in the North Atlantic in January. This implies amplification of the WN1 wave and results in the enhancement of the upward WN1 propagation from troposphere into stratosphere in January, leading to the weakened polar vortex in February-March. Although WN2 waves do not play a direct role in forcing the stratospheric vortex evolution, their tropospheric response to QBO-W/S_max conditions appears to be related to the maintenance of the NAO-like anomaly in the high-latitude troposphere in January. These results may provide a possible explanation for the mechanisms underlying the seasonal evolution of wintertime polar vortex anomalies during QBO-W/S_max conditions and the role of troposphere in this evolution.