The invention discloses a separated fiber reinforced plastic (FRP)-concrete-steel composite girder bridge structure and a construction method thereof. The structure comprises a steel girder, FRP boards provided with T ribs, and a reinforced concrete bridge deck, wherein the FRP boards are used as bottom plates of concrete at the rest of positions except the top surface of the steel girder, and are taken as templates used during pouring. The method comprises the steps of firstly, manufacturing and cutting standard FRP templates according to the line type of the transverse bridge direction of the bridge deck and the longitudinal length of a bridge, assembling a plurality of groups of separated FRP modules according to the line type of a cross section along the transverse bridge direction, then piecewise hoisting the separated FRP modules onto the steel girder to complete the assembly of the FRP templates of the whole bridge, and finally, pouring to form the concrete bridge deck. The composite girder bridge structure and the construction method thereof are suitable for a bridge deck form with any line type along the transverse bridge direction, and avoids the complicated connection treatment of three materials, i.e., FRP, concrete and steel at the same position, so that the construction difficulty of the FRP-concrete-steel composite girder bridge is reduced, and the bearing capacity and durability of the concrete bridge decks of the class of bridges are remarkably improved.