We present results of molecular dynamics simulations for hydroxide ion in supercritical water of densities 0.22, 0.31, 0.40, 0.48, 0.61, and 0.74 g/cc using the SPC/E water potential with Ewald summation. The limiting molar conductance of $OH^-$ ion at 673 K monotonically increases with decreasing water density. It is also found that the hydration number of water molecules in the first hydration shells around the $OH^-$ ion decreases and the potential energy per hydrated water molecule also decreases in the whole water density region with decreasing water density. Unlike the case in our previous works on LiCl, NaCl, NaBr, and CsBr [Lee at al., Chem. Phys. Lett. 1998, 293, 289-294 and J. Chem. Phys. 2000, 112, 864-869], the number of hydrated water molecules around ions and the potential energy per hydrated water molecule give the same effect to cause a monotonically increasing of the diffusion coefficient with decreasing water density in the whole water density region. The decreasing residence times are consistent with the decreasing potential energy per hydrated water molecule.