The invention discloses a movable formwork for construction of a large-span continuous beam and a construction method. The movable formwork comprises a bottom horizontal support system, a left main beam system, a right main beam system, crossbeam systems and outer mold systems. The left main beam system and the right main beam system are symmetrically mounted on the bottom horizontal support system and can synchronously move front and back on the bottom horizontal support system, the crossbeam systems are mounted on the main beam systems, and the outer mold systems are mounted on the crossbeam systems. The construction method includes a first step: beam manufacture; a second step: mold releasing; a third step: mold opening and traverse moving of the outer mold systems; a fourth step: longitudinal moving of a formwork; and a fifth step: repeating of the first step, the second step the third step and the fourth step by multiple times to sequentially complete follow-up construction of various hole beams. In the fourth step, the outer mold systems move to a pouring construction position of a next hole beam to realize mold closing. The movable formwork and the construction method have the advantages of reasonable design, fast construction speed, low construction cost, simplicity and convenience in utilization and operation, fine service effect, safety, reliability, and capability of effectively solving problems of complexity in construction process, high construction cost, slow construction progress, narrow application range and the like of an existing construction method for alarge-span continuous beam.