An anomalous increase of positron annihilation rare caused by a decrease of the temperature has been observed in supercritical fluid He-4 along isochors by an experiment. By using a molecular simulation, we demonstrate the similar increase in supercritical fluid xenon at the temperature that is far away from the liquid-vapor phase transition. The phenomenon can be interpreted as a sudden clustering of xenon atom that is induced by a self-trapping of the positron. (c) 2005 Elsevier B.V. All rights reserved.