The invention belongs to the technical field of bridge engineering, and discloses a curved surface rotary support. The technical proposal of the curved surface rotary support comprises the following: the curved surface rotary support comprises an upper support plate and a lower support plate which are fixedly connected with a beam body and a pier respectively through connecting mechanisms; the top surface of the lower support plate is a convex curved surface, and the bottom surface of the upper support plate is a concave curved surface corresponding to the convex curved surface of the lower support plate; the convex curved surface of the lower support plate or the concave curved surface of the upper support plate is embedded with a tetrafluorated slide plate; and the rotation of the support is realized by the sliding between the tetrafluorated slide plate embedded in the curved surface of the upper support plate or lower support plate and the corresponding lower support plate or upper support plate. The technical proposal overcomes the defect of unreasonable structure in the prior curved surface rotary support.