The invention discloses a full-bracket track-bogie bearing and moving device and a construction method for installing steel box girders. The device consists of a bracket system, a slideway longitudinal beam system, a splicing platform and a traction system; steel pipe buttresses in the bracket system are fixed on a treated foundation, the slideway longitudinal beam system is arranged on the bracket system, and mainly comprises two-slideway longitudinal beams, each of the two-slideway longitudinal beams is formed by connecting I-shaped rod pieces in an upper-lower parallel connection method, each side of the slideway longitudinal beam system is provided with one two-slideway longitudinal beam, and two two-slideway longitudinal beams are arranged totally on two sides; and berth bogies on the slideway longitudinal beam system slide on berth bogie tracks on the two-slideway longitudinal beams, and the berth bogies adopt a parallel connection mode and share one electric control switch to realize synchronous starting and closing. The bearing and moving device and the construction method have the beneficial effects that advantages of a large machinery hoisting method and a full-bracket jacking and sliding method are synthesized, the influence on ground traffic is less, the construction speed is fast, the cost is low, and the safety is high.