The chemical explosion of explosives wrapped with radioactive materials is a typical nuclear accident scenario. This study simulates and analyzes the process of a radioactive smoke cloud rising after the chemical explosion of an explosive device wrapped with plutonium materials. The state of the explosive products after the single-point detonation of the explosives was simulated. The numerical simulation of plutonium-aerosol rise was carried out based on the discrete phase model according to the simulation results of the chemical explosion. Based on the Chapman model and Levenberg–Marquardt algorithm, the simulation results of the plutonium aerosol-cloud height were fitted to obtain it as a function of time. The spatial distribution and velocity change of plutonium aerosol particles are analyzed. The reasons for the formation of vortex rings in the smoke cloud are discussed, which are significant in the emergency response to nuclear accidents.