Stratospheric aerosol geoengineering has been proposed as a potential solution to reduce climate change and its impacts. Here, we explore the responses of the Hadley circulation (HC) intensity and the intertropical convergence zone (ITCZ) using the strategic stratospheric aerosol geoengineering, in which sulfur dioxide was injected into the stratosphere at four different locations to maintain the global-mean surface temperature and the interhemispheric and equator-to-pole temperature gradients at present-day values (baseline). Simulations show that, relative to the baseline, strategic stratospheric aerosol geoengineering generally maintains northern winter December–January–February (DJF) HC intensity under RCP8.5, while it overcompensates for the greenhouse gas (GHG)-forced southern winter June–July–August (JJA) HC intensity increase, producing a 3.5 ± 0.4% weakening. The residual change of southern HC intensity in JJA is mainly associated with stratospheric heating and tropospheric temperature response due to enhanced stratospheric aerosol concentrations. Geoengineering overcompensates for the GHG-driven northward ITCZ shifts, producing 0.7° ± 0.1° and 0.2° ± 0.1° latitude southward migrations in JJA and DJF, respectively relative to the baseline. These migrations are affected by tropical interhemispheric temperature differences both at the surface and in the free troposphere. Further strategies for reducing the residual change of HC intensity and ITCZ shifts under stratospheric aerosol geoengineering could involve minimizing stratospheric heating and restoring and preserving the present-day tropical tropospheric interhemispheric temperature differences.