In the study, the total conductivies in [(Ce $O_2$)$_{1-x}$ (Zr $O_2$)$_{x}$]$_{0.8}$(Sm $O_{1.5}$)$_{0.2}$ (x- 0, 0.05, 0.1, 0.2) solid solution were measured as a function of temperature and oxygen partial pressure between 80$0^{circ}C$ and 1,00$0^{circ}C$ using 4-probe d.c method. Under pure oxygen atmospere, the oxygen ionic conductivity of [(Ce $O_2$)$_{1-x}$ (Zr $O_2$)$_{x}$]$_{0.8}$(Sm $O_{1.5}$)$_{0.2}$ decreased with the concentration of Zr $O_2$At high oxygen partial pressure, the electrical conductivity is almost independent of oxygen partial pressure and decreased with the increase in Zr content. However, the electrical conductivity increase with decreasing oxygen partial pressure and is almost independent of Zr content at low oxygen partial pressure. Empirically, Total conductivity( $sigma$ ) was expressed by the p$o_{2}$ -independent conductivity as $sigma$$_{i}$, and the $p_{-1/4}$ $o_{2}$sup -dependent part as $sigma$$_{e}$. Total, ionic and electronic conductivities fitted by data enabled to determine the transference number. The ionic transference number( $t_{i}$ ) decreased while the electronic transference( $t_{e}$ ) increase with the increase in Zr content and p$o_{2}$