An Hg- or Nd-based oxide superconductor comprises Ba as a constituent element and has a content of carbon as an impurity at a level of not greater than 2.0 atomic % whereby the oxide superconductor stably shows high superconducting characteristics without causing degradation with time. For its production, BaO, which has a reduced content of carbon impurity of 0.5% or below, is provided as a feed stock for Ba, and the starting materials are mixed and processed in a dry atmosphere wherein an amount of a carbon-containing gas is suppressed to a certain level, thereby obtaining the oxide superconductor.