Airborne dust is the main climatic agent in the Martian environment. Local dust storms play a key role in the dust cycle; yet their life cycle is poorly known. Here we use mesoscale modeling that includes the transport of radiatively active dust to predict the evolution of a local dust storm monitored by OMEGA on board Mars Express. We show that the evolution of this dust storm is governed by deep convective motions. The supply of convective energy is provided by the absorption of incoming sunlight by dust particles, rather than by latent heating as in moist convection on Earth. We propose to use the terminology "rocket dust storm", or conio-cumulonimbus, to describe those storms in which rapid and efficient vertical transport takes place, injecting dust particles at high altitudes in the Martian troposphere (30–50 km). Combined to horizontal transport by large-scale winds, rocket dust storms produce detached layers of dust reminiscent of those observed with Mars Global Surveyor and Mars Reconnaissance Orbiter. Since nighttime sedimentation is less efficient than daytime convective transport, and the detached dust layers can convect during the daytime, these layers can be stable for several days. The peak activity of rocket dust storms is expected in low-latitude regions at clear seasons (late northern winter to late northern summer), which accounts for the high-altitude tropical dust maxima unveiled by Mars Climate Sounder. Dust-driven deep convection has strong implications for the Martian dust cycle, thermal structure, atmospheric dynamics, cloud microphysics, chemistry, and robotic and human exploration.