The simulated and the experimental electrical conductivity of ionic conductor composites (Al2O3/yttria-stabilized zirconia) either containing different amounts (5 and 50 wt.%) of alumina or having the same amount of insulating phase (10 wt.%) with different grain sizes are presented and compared. A digital image-based modelling procedure to simulate the electrical behaviour of the composites was used here. The method works, generating. by the Voronoi tessellation technique in which a genetic algorithm is used, two-phase polyhedral microstructures and then converting them into a random electrical network. The real and imaginary part of the electrical network impedance was computed by the transfer matrix method. The model is able to reproduce the experimental results well.