The invention discloses a composite corrugated steel web box girder and a construction technology of the composite corrugated steel web box girder. The composite corrugated steel web box girder comprises a bottom flange plate, a top flange plate and two corrugated steel webs which are symmetrically supported between the bottom flange plate and the top flange plate. A prestress system is arranged in the bottom flange plate and comprises a middle prestress structure and two side prestress structures. The construction technology of the composite corrugated steel web box girder comprises the steps of (1) arranging and installing the prestress system and the corrugated steel webs; (2) constructing the bottom flange plate, wherein the construction of the bottom flange plate comprises the steps that firstly, pouring of concrete in the middle of a part of sections of the bottom flange plate and primary prestress tension are conducted, and secondly, pouring of concrete in the middle of the remaining sections of the bottom flange plate and secondary prestress tension are conducted; (3) constructing the top flange plate before construction of the bottom flange plate or in the process of construction of the bottom flange plate or after construction of the bottom flange plate. According to the composite corrugated steel web box girder and the construction technology of the composite corrugated steel web box girder, the design is reasonable, construction is convenient, the constructed and formed composite corrugated steel web box girder is reasonably stressed and good in use effect, and multiple kinds of problems of an existing concrete box girder can be solved.