Stratospheric water vapour (SWV), as a greenhouse gas, modulates the radiative energy budget of the climate system. It is sensitive to, and plays a significant role in the climate change. In this study, we investigate the SWV response to CO2 increase with the Whole Atmosphere Community Climate Model (WACCM). In addition, we study its possible feedback on stratospheric temperature and relevant mechanisms. In our model experiments, the CO2 concentration and sea surface temperature (SSTs) are changed at the same time, as well as separately, to enable separating the radiative-photochemical and dynamical response to CO2 doubling scenarios. The model results show that the response of SWV to CO2 doubling is dominated by the changes in the SSTs, with an increase of the SWV concentration by similar to 6 to 10% in most of the stratosphere and more than 10% in the lower stratosphere, except for winter pole in the lower stratosphere, where the CO2 doubling decreases water vapour. The increase of SWV is mostly due to a dynamical response to the warm SSTs. Doubled CO2 induces warm SSTs globally and further leads to moist troposphere and a warmer tropical and subtropical tropopause, resulting in more water vapour entering stratosphere from below. As a greenhouse gas, large increase of SWV in the lower stratosphere, in turn, affects the stratospheric temperature, resulting in a warming of the tropical and subtropical lower stratosphere, offsetting the cooling caused by CO2 doubling.