The invention relates to a novel method for constructing capping beams of bridges, and discloses a method for constructing capping beams of bridges on the basis of a formwork and support integrated device. The formwork and support integrated device comprises a bottom formwork, an end formwork and two side formworks. The method includes machining the bottom formwork, the end formwork and the side formworks according to the sizes of the capping beams; constructing piers so that the heights of the piers are equal to preset heights, and embedding brackets on two sides of the top of each pier; mounting the formworks after design requirements on the concrete strength of the piers are met, respectively hoisting the two side formworks onto the brackets on the two sides of each pier at first, then respectively hoisting and mounting the bottom formwork and the end formwork and fixing both the bottom formwork and the end formwork onto side form trusses; pouring capping beam concrete in the built formworks. The side formworks comprise the side form trusses and side form panels. The method has the advantages that the side form trusses can completely bear dead weight of the concrete and construction load of the concrete when the capping beam concrete is poured, so that individual supports can be omitted, the construction period can be effectively shortened, and the cost can be saved.