Three-dimensional microstructure of mixed ionic and electronic conducting cathode, La0.6Sr0.4Co0.2Fe0.8O3-delta (LSCF6428), is obtained by a dual-beam focused ion beam-scanning electron microscope, and its overpotential is predicted by the lattice Boltzmann method. Gaseous, ionic and electronic transport equations coupled with electrochemical reaction at the gas/solid interface in the three-dimensional microstructure are solved with an assumption of local equilibrium in the solid oxide. The gas transport is modeled by the dusty gas model. The numerical simulation is conducted under the current density conditions of 0.01, 0.05, 0.1 and 0.2 A/cm(2). Predicted cathode overpotentials agreed well with the experimental results. However, predicted overpotential was very large at O-2 = 20%, T = 973 K and i = 0.2 A/cm(2) case due to the decline of ionic conductivity at low oxygen partial pressure. Three-dimensional chemical potential and current vector distributions inside LSCF microstructure are presented. Ionic and electronic current stream lines are uniform and smooth, which indicates good ionic and electronic conductions as well as wide electrochemically active areas inside the LSCF microstructure. Present method will be an effective tool for investigating local oxygen potential field which affects local reactions, diffusions and physical properties of the MIEC cathodes. (C) 2010 Elsevier B.V. All rights reserved.