A numerical simulation of Rayleigh–Bénard convection with supercritical carbon dioxide is presented in this paper. A shallow cavity with an aspect ratio of 4 is selected as a container that is fully filled with supercritical carbon dioxide. The influences of the bottom heat flux on the flow stability, flow pattern evolution, and heat transfer ability of Rayleigh–Bénard convection are analyzed. Meanwhile, the transient and steady-state fluid behaviors are obtained. The results show that the bottom heat flux plays a dominating role in the stability of the convection. A transition from stable evolution to significant oscillation is found with the increase of the heat flux. The flow pattern evolution also strongly relies on the heat flux. A four-cell structure to a six-cell structure transformation accompanied by the orderly multicellular flow is observed with increasing heat flux. In addition, the local Nusselt number on the bottom wall is strongly related to the cell structure in the cavity.