An ozone generating apparatus according to one embodiment includes a hollow cylindrical sealed container provided with an inlet for a feed gas containing oxygen gas and an outlet for an ozonized gas. A discharge tube including a dielectric tube arranged within the container and a first electrode arranged within the dielectric tube is provided in the container. A second electrode is arranged within the container and surrounds the first electrode, spaced apart from the dielectric tube to form a discharge gap between the second electrode and the dielectric tube. The apparatus further includes a discharge voltage source configured to apply a discharging voltage across the first and second electrodes, and a cooling water jacket surrounding the second electrode. The dielectric tube has an outer diameter of 12 mm or more, but 19 mm or less.