The invention discloses a viscous, elastic and anti-buckling brace combined damper. The damper sequentially comprises a steel plate in the center, an annular inner steel cylinder and an annular outer steel cylinder from inside to outside, the steel plate is sleeved with the annular inner steel cylinder, the annular inner steel cylinder is sleeved with the annular outer steel cylinder, the portion between the annular inner steel cylinder and the annular outer steel cylinder is filled with a viscous and elastic material layer, and the annular inner steel cylinder, the viscous and elastic material layer and the annular outer steel cylinder are connected in a high-temperature high-pressure vulcanization mode. The damper further comprises an upper anchoring plate and a lower anchoring plate which are opposite to each other. The steel plate is composed of an upper end, a buckling section and a lower end, two grooves I are symmetrically formed in the upper end in the horizontal direction, the upper anchoring plate is fixedly embedded in the grooves I, two grooves II are symmetrically formed in the lower end in the horizontal direction, the lower anchoring plate is embedded in the grooves II, the lower anchoring plate can slide up and down in the grooves II relative to the grooves II, the annular outer steel cylinder is fixedly connected with the lower anchoring plate, and the annular inner steel cylinder is fixedly connected with the upper anchoring plate. The diameter of the annular inner steel cylinder is 1-3 mm larger than the horizontal length of the steel plate.