Stability of natural convection in porous media differs from that in Newtonian fluid due to the changes of the thermal inertia and the friction. This paper aims to investigate the natural convection and its stability in a toroidal thermosyphon filled with porous media. The flow and temperature fields were numerically simulated and compared with that of Newtonian fluid. The results predicted two obvious local reversal flows near the connections of heating and cooling halves. A one-dimensional model was proposed which described qualitatively the occurring and stability of the thermal convection. The model suggested that the flow stability depends largely on the Prandtl number. The global flow can probably be chaotic only if the Prandtl number is finite. Contradictions of the conclusions drawn by different researchers were also discussed.