$Gd_2O_3$-doped $CeO_2$ (GDC) and $La_{0.6}Sr_{0.4}Co_{0.2}Fe_{0.8}O_3$ (LSCF) composite cathode materials were prepared in order to be applied to intermediate-temperature solid oxide fuel cells. The electrochemical polarization was evaluated using ac impedance spectroscopy involving geometric restriction at the interface between an ionic electrolyte and a mixed-conducting cathode. In order to optimize the cathode composites applicable to a GDC electrolyte, the cathode composites were evaluated in terms of polarization losses with regard to a given electrolyte, i.e., GDC electrolyte. The polarization increased significantly with decreasing temperature and was critically dependent on the compositions of the composite cathodes. The optimized cathode composite was found to consist of GDC 50 wt% and LSCF 50 wt%; the corresponding normalized polarization loss was calculated to be 0.64 at $650^{circ}C$.