A fixing structure of a faucet is fixed on a sink countertop with a hole and contains a faucet having a housing, a pull-out spray head, a mixing valve, and a water supply set. The water supply set includes a cold-water inlet pipe, a hot-water inlet pipe, and a mixing outlet pipe. A positioning device includes a base having a peripheral fence, a bottom fence, and a mouth. The bottom fence has a limiting face and at least one orifice, the limiting face has a channel, two stop posts, and an abutting face. Two screw rods extend out of the hole and are rotated above the base. Two clamping blocks are screwed with the two screw rods and are limited by the two stop posts to rotate when the two screw rods are rotated, and the two clamping blocks move upwardly to retain a bottom end of the sink countertop.