A simple mathematical model is established to predict the self-discharge process in a kilowatt-class vanadium redox flow battery stack. The model use basic mass transport theory to simulate the transfer of vanadium ions in the battery. The simulation results agree reasonably with the experimental values, confirming the validity of the model. It is found that the diffusion rate of vanadium ions depends on the diffusion coefficient, the partition coefficient and the concentration gradient of the vanadium ions between the two half cells. For the self-discharge process at the initial SOC of 0, the net transfer direction of vanadium ions is towards the negative electrolyte until the diffusion flux of V3+ becomes larger than that of VO2+. For the self-discharge process at the initial SOC of 65%, the net transfer direction of vanadium ions is towards the positive electrolyte at the initial 20h and then turns to the negative electrolyte. There are two obvious changes in the diffusion flux of vanadium ions at about 33h and 43h, corresponding to the vanishing time of VO2+ and V2+ respectively. (C) 2010 Elsevier B.V. All right reserved.