The invention discloses a device and construction method for limiting lateral displacement and overturn of a curve beam bridge. At least one lateral displacement and overturn prevention unit is arranged between the beam bottom of a box beam and a pier. Each lateral displacement and overturn prevention unit comprises an inner component and an outer component, wherein the outer component is arranged at the bottom of the beam bottom of the box beam, and the inner component is arranged on the pier; the position between the inner component and the outer component is filled with a rubber base plate; at least one fixing anchor rod is arranged at the position where the inner component is opposite to the outer component; and one end of each fixing anchor rod is provided with a yielding mechanism. The inner components and the outer components are mounted on the beam bottom of the box beam and the pier, arranged on the two sides of a beam support, mutually embedded and fixed through the rubber base plates, and used for mutually limiting excessive lateral displacement of the beam bottom of the box beam due to bending-twisting coupling force to prevent a beam body from overturning; and meanwhile, the rubber base plates arranged between the inner components and the outer components are used for relieving horizontal displacement through elastic deformation, and can achieve an excellent buffering and damping effect.