This paper develops particle-resolved simulations to predict conductivity within porous composite electrodes. Hundreds of spherical particles (order fractions of a micron) are packed randomly into a cubical region (order of a few microns), using two alternative packing algorithms. The composite structures include both ion-conducting and electron-conducting particles. The particle network is discretized using tetrahedral meshes that fully resolve the interiors of the particles and their intersections. Charge-conservation equations are solved to predict current through the network. These simulations are used to derive the effective conductivities that are required for macroscale simulations at length scales much larger than the particle scale. Because the microstructures are synthesized via random particle packing, multiple realizations are needed to deliver statistically invariant results. The results show that a few hundred particles with a few hundred realizations is sufficient. Predicted coordination numbers, percolation probabilities, and three-phase-boundary lengths are consistent with percolation theory, but the predicted effective conductivities are significantly smaller than those predicted with conventional percolation theory. By adjusting the Bruggeman factor from the conventional value of 1.5-3.5 brings the percolation-theory prediction for effective conductivity in line with the fully resolved results. (C) 2010 Elsevier BM. All rights reserved.