This paper demonstrates a possible application of the so-called CANDLE concept, namely solitary breeding/burning wave concept, in a supercritical water cooled fast reactor (SCWFR). The high enthalpy increment and the large density variation of the supercritical water through the core are favourable to this concept. However, based on an SCWFR design, it is found that only the Th-U conversion cycle offers the possibility of a solitary breeding/burning wave without using a burnable poison. A one-group diffusion equation coupled with simplified burn-up equations is investigated for the burn-up drift wave problem, where the coupling with the thermal hydraulics of the supercritical water, especially the dependence of microscopic cross sections on the water density, and consequently on the neutron fluence, is also taken into account. A specific example of the solitary breeding/burning wave in the one-dimensional case is obtained numerically and presented in this paper. The asymptotic burn-up is about 33 at.%. Besides usual advantages of the CANDLE concept, e.g. low reactivity swing and high fuel utilization, the negative coolant feedback is an inherent feature of this kind of reactor concept. (C) 2010 Elsevier Ltd. All rights reserved.