The ability to transport both ionic and electronic species is one of the most important properties of a mixed ionic-electronic conductor for electrosynthesis, gas separation, and electrode applications. In this paper, resistor network approach is used to predict the effective conductivities of a composite mixed conductor consisting of any number of randomly-distributed phases. The model is further used to predict the effective ionic, electronic, and ambipolar transport behavior of two-phase and three-phase composite mixed conductors as a function of the volume fraction of each randomly-distributed constituent phase. Results indicate that the optimum ambipolar conductivity occurs only within certain volume fractions of the constituent phases, depending on their relative ionic and electronic conductivities.