We studied the local-ion-hopping mechanism of oxygen ions (vacancies) in SC3+ -doped ZrO2 by measuring the quasielastic light scattering (QELS) as well as the electrical conductivity. The activation energy in the cubic phase obtained by means of fixed-frequency measurement of the QELS intensity was 0.55 eV and can be ascribed to the oxygen vacancy hopping around the dopant cation(s) (Sc3+). The activation energy obtained from the electrical conductivity was 0.83 eV in the cubic phase and 0.95 eV in the rhombohedral phase. The activation energy in the cubic phase is considered to reflect oxygen vacancy hops from one SC3+ trap to another. One reason for the high electrical conductivity in SC3+-doped ZrO2 is considered to be the vacancy's freedom to change sites around the Sc3+ traps, which allows it to easily find the hopping path from one trap to another having the minimum activation energy.