The invention discloses a condensate oil desulphurization stabilizing apparatus and a method thereof. The apparatus comprises an unstable condensate oil flash evaporation tank, an unstable condensate oil filter, a primary heat exchanger, a three-phase separator, a secondary heat exchanger, a condensate oil desulphurization stabilizing tower, a tower bottom reboiler and a stable condensate oil transfer pump. Fuel gas is introduced to the bottom of the condensate oil desulphurization stabilizing tower as a gas stripping gas to remove parts of organic sulfur in unstable sulfur-containing condensate oil, and a stripping technology is adopted to remove light components in the condensate oil to make the hydrogen sulfide content and the saturated steam pressure of the condensate oil meet national standards and other requirements. A flow-through technology and a shunting technology are determined according to the feeding mode of the desulphurization stabilizing tower, the shunting technology is more economic when the treatment scale of the condensate oil treatment apparatus is not smaller than 100t/d, and the flow-through technology is more suitable for the apparatus with a small treatment scale.