The natural convection of supercritical carbon dioxide is numerically studied by using a variable-property thermal lattice BGK model. Effects of the special property variation on both heat transfer and flow features are discussed. It is found that the special thermo-physical properties around the pseudo-critical temperature are favorable for the convection motion and heat transfer of supercritical carbon dioxide. It is also found that the variations in the operating pressure and the heat sink temperature both have significant effects on the heat transfer rate. The optimization problem about the operation condition of supercritical carbon dioxide in convection-based energy systems does exist. Operation under the optimal condition helps to enhance convective heat transfer rate greatly.