The invention discloses an offshore bridge girder erection machine and a construction method thereof, and relates to the technical field of offshore platform construction. The construction method of the offshore bridge girder erection machine comprises the steps of bridge girder erection machine assembling, bridge girder erection machine testing, bridge girder erection machine in-place placing, prefabricated part installing and bridge girder erection machine moving. According to the construction method of the offshore bridge girder erection machine, improvement is performed on the basis of bridge girder erection machines for highways and railways, a front supporting leg structure of the bridge girder erection machine is transformed, and is suitable for requirements for different steel pipepile intervals and loads; meanwhile, the transition joints are arranged on the steel pipe piles of the front supporting legs, and the function of front-back and left-right adjustment is achieved so as to adapt to the horizontal construction deviation of the steel pipe piles or the concrete piles on the lower portion; the middle supporting leg structure is improved, so that the middle supporting leg structure can adapt to the characteristic that steel bars on pier caps at the tops of steel pipe piles are complex, water operation is changed into road construction finally, influences of adversefactors such as surges and tides are reduced, meanwhile, the construction progress is accelerated, the installation quality is improved, and the construction cost is reduced.