A simple but physicochemically meaningful numerical model of a solid oxide fuel cell (SOFC) anode is developed as a tool to understand and reproduce its impedance spectra. The model considers conservations of electrons, ions and gas species within the anode, which are coupled by a non-linear electrochemical reaction model. The developed model is first calibrated by impedance spectra that are experimentally obtained at the open circuit conditions at several temperatures, by adjusting the ionic conductivity, exchange current density and electrostatic capacitance. All of these parameters are confirmed to be within an acceptable range of values found in literature. Also, real anode microstructural parameters obtained by three-dimensional FIB-SEM imaging is implemented to eliminate any other arbitrary fitting parameters from the model. Then, the model is used to reproduce impedance spectra obtained from another anode with different microstructure and also those measured at polarized conditions and at different temperatures, and gives good agreement with the experimental results. Considering the computational resources required to reproduce impedance spectra, the developed model is expected to be used as an alternative to the conventional equivalent circuit fitting.