Based on the Thiele's approach, we investigate current-induced oscillation of a magnetic domain wall. A special attention is paid to effect of damping enhancement due to magnetization dynamics in the limit of no spin diffusion. Unlike for a translation motion, the enhanced damping due to magnetization dynamics has an important role for a rotational motion of a magnetic domain wall and can significantly reduce its oscillation frequency. The frequency reduction becomes more substantial for a narrower domain wall. This result provides a design strategy of high-frequency devices utilizing domain wall oscillation. (C) 2010 Elsevier B.V. All rights reserved.