A three-dimensional (3-D) model for H2/Br2 redox flow batteries (RFBs) is developed by rigorously accounting for the redox reactions of hydrogen and bromine species, and the resulting species and charge transport through various cell components. First, the H2/Br2RFB model is experimentally validated against the discharge and charge voltage curves measured over a wide range of current densities up to 1.4 A cm−2. In general, the model predictions compare well with the experimental data, and they further reveal key electrochemical and transport phenomena inside the cell. Particular emphasis is placed on analyzing the crossover of bromine species through the membrane at detailed levels where the model calculates electro-osmotic and diffusive fluxes of bromine species across the membrane; the relative magnitudes are compared under various charging and discharging stages. In addition, a parametric study is carried out to examine the effects of two key design variables on cell performance and crossover behavior, i.e., the thicknesses of the membrane and bromine porous media. This full 3-D H2/Br2 RFB model can be applied to realistic large-scale cell geometry for grid-scale energy storage applications and directly utilized to determine the optimal design and operating conditions for H2/Br2 RFBs.