A comprehensive numerical model was developed to predict the electrochemical performance of solid oxide fuel cell (SOFC). The multi-component Lattice Boltzmann (LB) model based on kinetic theory for gas mixtures combined with a representative elementary volume (REV) scale LB algorithm based on the Brinkman equation for flows in porous media, the Butler-Volmer equation and Ohm's law were adopted to deal with the concentration, activation and ohmic overpotentials, respectively. The volt ampere characteristics were calculated and compared with those obtained by the existing electrochemical model, as well as the experimental data. It was shown that the electrochemical model given by this paper was capable of describing the electrochemical performance much more accurately because of the kinetic nature of the LB method which was based on microscopic models and mesoscopic kinetic equations for fluids, and the accurate prediction of multi-component mass transfer in SOFC porous electrodes affected the simulation of the cell electrochemical performance significantly. Moreover, the effects of different electrode geometrical and operating parameters on the cell performance were investigated. The developed electrochemical model based on LB algorithm at REV scale is useful for the design and optimization of SOFC. (C) 2014 Elsevier Ltd. All rights reserved.