During the past decades, concurrent with global warming, most of global oceans, particularly the tropical Indian Ocean, have become warmer. Meanwhile, the Southern Hemispheric stratospheric polar vortex (SPV) exhibits a deepening trend. Although previous modeling studies reveal that radiative cooling effect of ozone depletion plays a dominant role in causing the deepening of SPV, the simulated ozone-depletion-induced SPV deepening is stronger than the observed. This suggests that there must be other factors canceling a fraction of the influence of the ozone depletion. Whether the tropical Indian Ocean warming (IOW) is such a factor is unclear. This issue is addressed by conducting ensemble atmospheric general circulation model (AGCM) experiments. And one idealized IOW with the amplitude as the observed is prescribed to force four AGCMs. The results show that the IOW tends to warm the southern polar stratosphere, and thus weakens SPV in austral spring to summer. Hence, it offsets a fraction of the effect of the ozone depletion. This implies that global warming will favor ozone recovery, since a warmer southern polar stratosphere is un-beneficial for the formation of polar stratospheric clouds (PSCs), which is a key factor to ozone depletion chemical reactions.