Natural convective flow of supercritical fluid has become hot topic both in scientific research and engineering applications. Natural circulation thermosyphon using supercritical/trans-critical CO2 can be a potential substitute for effective transportation of heat and mass without valves/pumping devices. This paper presents numerical investigations into the effect of unsteady heat input on the trans-critical CO2 thermosyphon, including sudden/quick increase of heat input, gradual/slow increase of heat input and sudden decrease of heat input. Those unsteady input situations are often seen in real applications and have become the core problem of efficiency and safety improvement. In the present study, two-dimensional rectangular natural circulation loop model is set up and numerically investigated. New heat transport model aiming at trans-critical thermosyphon heat input and system stability laws is proposed with supercritical/trans-critical turbulence model incorporated. It is found that when compared with supercritical CO2 condition, trans-critical CO2 thermosyphon has quite different behaviors. Natural convective thermosyphon stability is found to be of routinely dependent for different heat input change mode. Stability factors of natural convective trans-critical CO2 flow and its implications on real system control are also discussed in this paper. (C) 2012 Elsevier Ltd. All rights reserved.