Mid to low frequency impedance for a cathode in a lithium ion battery (LIB), which is affected by lithium-ion diffusion into active materials, was investigated. We had earlier suggested that charge-transfer and diffusion impedances are attributed to a particle size distribution for a commercially available LIB, and we designed an equivalent circuit in which two series circuits of charge-transfer resistance and Warburg impedance were connected in parallel. Here, to validate the design of the equivalent circuit, the secondary-particle size distribution of the LiNi1/3Mn1/3Co1/3O2 cathode in a lab-made LIB, in which the secondary-particles were controlled into wide and narrow distribution by sieving, was investigated by electrochemical impedance spectroscopy. The equivalent circuit was designed in which series circuits of charge-transfer resistance and Warburg impedance were connected in parallel. Dependency of impedance response on the number of parallels of the series circuits was evaluated for the cathodes using different secondary-particle size distributions of the active material. Additionally, the tendency of change in the charge-transfer resistance and the limiting capacitance was discussed from the standpoint of secondary-particle size distribution. The results confirm the effectiveness of the designed equivalent circuit which reflects the secondary-particle size distribution of cathode active materials.