Battery positive-electrode material is usually a mixed conductor that has certain electronic and ionic conductivities, both of which crucially control battery performance such as the rate capability, whereas the microscopic understanding of the conductivity relationship has not been established yet. Herein, we used Boltzmann transport theory and molecular dynamics at the ab initio level to investigate the electronic and ionic conductivities on the same footing, with the representative layered oxides Lix(Co, Ni)O2. The present calculations successfully demonstrated the electronic conductivities quantitatively and indicated a microscopic origin of the electronic difference between LixCoO2 and LixNiO2 (0.6 < x≤ 1). The calculated ionic conductivities were also consistent with the experimental values. Especially, we observed Ni ion migration to the Li layer at lower x, leading to suppression of Li ion diffusion. Based on these results, we found that the ratio and product of the electronic and ionic conductivities as ζ and κ, respectively, are good descriptors to evaluate the battery positive-electrode performance because these descriptors clearly can distinguish between LixCoO2 and LixNiO2. Referring to the values of the excellent positive electrode LixCoO2, we suggest ζ≈ 106 and κ≈ 10−2 as target measures for the positive-electrode material design.