A two-dimensional transient model for a passive thermal management system was developed for commercial square lithium ion battery by using the phase change material (PCM) of paraffin saturated in metallic copper foam. This model combined the thermo-electrochemical model for the battery and a model that characterized the solid–liquid phase change of paraffin in copper foam. The thermo-electrochemical model was composed of species conservation, charge conservation, and energy balance equations. In the model of phase change in metal foam, the non-Darcy, natural convection of melted paraffin, and local thermal non-equilibrium effects were considered. The thermo-electrochemical performance of the battery and convective heat transfer behavior of the foam-PCM composite were investigated. The predicted results were in agreement with experimental data. Compared to the air convection and adiabatic modes, the thermal management by foam-PCM composite has dramatically reduced battery surface temperature to the allowable range at 1C and 3C discharge rates. •Theoretical model for passive thermal management of Li-ion battery was developed.•Battery temperature exceeded safety value under isothermal and air convection modes.•Inclusion of paraffin and foam significantly reduced battery surface temperature.•Natural convection of melted paraffin was greatly constrained in foam matrix.•Temperature difference between foam and PCM validated energy two-equation model.