A two-dimensional multicomponent 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 is developed to simulate the mass transport in the porous anode and cathode of solid oxide fuel cell (SOFC). The concentration overpotential is calculated and compared with that obtained by the extended Fick's model (FM), the dusty gas model (DGM), and the Stefan Maxwell model (SMM), as well as the experimental results. It is concluded that LB method is a much more accurate method for the simulation of mass transfer within fuel cell electrodes. Moreover, the effects of different electrode geometrical and operating parameters on concentration polarization are also investigated.