The summertime Sahara and Sahel are the world’s largest source of airborne mineral dust. Cold-pool outflows from moist convection (‘haboobs’) are a dominant source of summertime uplift but are essentially missing in global models, raising major questions on the reliability of climate projections of dust and dust impacts. Here we use convection-permitting simulations of pan-African climate change, which explicitly capture haboobs, to investigate whether this key limitation of global models affects projections. We show that explicit convection is key to capturing the observed summertime maximum of dust-generating winds, which is missed with parameterised convection. Despite this, future climate changes in dust-generating winds are more sensitive to the effects of explicit convection on the wider meteorology than they are to the haboobs themselves, with model differences in the change in dust-generating winds reaching 60% of current values. The results therefore show the importance of improving convection in climate models for dust projections.