It is well known that stabilized zirconia exhibits long-range transport of oxygen ions which gives rise to diffusion relaxation of oxygen vacancies. The internal friction and the change in sound velocity in single-crystal calcia-stabilized zirconia (CSZ) doped with 12 mol % CaO were measured for longitudinal sound waves in the frequency range from 20 Hz to 700 Hz using a vibrating reed technique. In the temperature range from 300 K to 700 K, the relaxation strength exhibits strong anisotropy with respect to the directions of the k vectors. As the frequency increases the internal friction peak and the change in sound velocity shift toward high temperature, and the relaxation strength remains constant. The results show that a smaller number of oxygen vacancies contribute to diffusion relaxation than to localized relaxation, which is attributed to hopping of bound oxygen vacancies within the local structure. Comparison of the results with those reported previously for yttria-stabilized zirconia (YSZ) doped with 9.5 mol % ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$, suggests that oxygen vacancies are more strongly bound by the local structure in CSZ than in YSZ.