The invention discloses an internal prestress steel and concrete combined simply supported girder bridge of a prefabricated and assembled fish-bellied corrugated steel web and a construction method thereof. A prefabricated fish-bellied corrugated steel web girder and a prefabricated concrete bridge deck are adopted, a ladle concrete component is adopted at the lower flange of the fish-bellied corrugated steel web girder, and prestress is stretched in concrete of the ladle concrete component at the lower flange. A web is in a fish-bellied corrugated shape, so that the weight of the bridge can be greatly reduced; the ladle concrete component is adopted at the lower flange, and a prestressing duct is reserved so as to stretch the prestress, so that the stiffness and bending resistance of the corrugated steel web girder are obviously improved, the problem of air exposure of externally prestressed tendons of the corrugated steel web combined girder is solved, and thus the durability and reliability of the prestressed tendons are greatly improved. Meanwhile, the prestress steel and concrete combined simply supported girder of the corrugated steel web with the structure can be conveniently transported, prefabricated and assembled and can completely meet the requirements of factory-made components and quick field installation. Accordingly, the inventors also establish a corresponding construction method which is safe, convenient and quick in construction.