This paper develops a computational model that resolves the complex three-dimensional microstructure of Li-ion battery cathodes. The microstructural geometry is reconstructed from focused-ion-beam–scanning-electron-microscopy (FIB-SEM) experiments. Raw data from FIB-SEM experiments are processed into finite-volume discretizations that are directly suited for three-dimensional computational simulation. The model represents transport and electrochemistry within the solid phase of the electrode structure. The results predict the temporally and spatially varying Li concentrations and electrostatic potentials within the solid-phase electrode material (e.g., LiCoO2) as functions of discharge rate. The models predict global discharge characteristics that are consistent with experiment. Moreover, the results reveal significant three-dimensional spatial variations within the actual electrode structure that cannot be predicted with models based on idealized microstructures such as spherical electrode particles.