Abstract: In order to illuminate the distribution of electron potential energy of ignited cesium thermionic energy converter (TEC), differential transport equations based on kinetic method were built to describe the transport of the low-temperature and weakly ionized plasma in the interval of the electrodes. And the boundary conditions were selected by analysis of the electron potential energy in the plasma sheath. Then, the adaptive computer program based on Newton iteration algorithm was designed to solve the transport equations and boundary conditions. It is found that the calculated U-I characteristic accords with lecture result and the potential jump in the emitter sheath changes from non-monotonic to monotonic shape with the increase of the current density, while the potential jump in the collector sheath changes sign.