Anomalously high ionic mobilities of H+ and $OH^-$ are owing to the transfer of $H^+$ by the Grotthus chain mechanism. Molecular dynamics simulations for the system of 215 water including $OH^-$ ion at 298.15 K using the OSS2 model [J. Chem. Phys. 109, 5547 (1998)] as a dissociable water model with the use of Ewald summation were carried out in order to study the dynamics of $OH^-$ in water. The calculated ionic mobility of $OH^-$ is in good agreement with the experimental result and the Grotthus chain mechanism is fully understood.