The invention relates to a catalytic ozonation treating apparatus and process for refractory organic wastewater. The apparatus comprises a catalytic oxidation tower, an ozone generator connected with the bottom inlet of the catalytic oxidation tower and a tail gas treating and recycling system connected with the top outlet of the catalytic oxidation tower, wherein the outlet of the tail gas treating and recycling system is connected with the inlet of the ozone generator, and the tail gas treating and recycling system comprises a carbon dioxide absorbing tower, a drying unit and an oxygen storage tank which are successively connected. According to the invention, high-concentration ozone is generated from pure oxygen via the ozone generator, macro-molecular refractory organic pollutants in the organic wastewater is subjected to catalytic ozonation in the catalytic oxidation tower, and tail gas is treated by the tail gas treating and recycling system and then cyclically used as a gas source for the ozone generator; carbon dioxide and steam are removed through the tail gas treating and recycling system, so tail gas is purified, secondary pollution is avoided, the utilization rate of oxygen is improved, and treating cost is reduced.