A construction method of a steel composite girder bridge includes installing steel girders on piers and forming shearing connectors on the steel girders at intervals of a predetermined distance, installing stagings and a first form for casting deck concrete in the steel girders, installing non-composite members in an upper flange of the steel girders to form each non-composite section of supporting points, installing a second form around each of the shearing connectors to form a shearing pocket, arranging sheath pipes in the supporting points and forming supporting point decks by casting and curing concrete, applying pre-stress to each section of the supporting point decks through the sheath pipes and performing a grouting process, forming span decks adjacent to the supporting point decks by casting and curing concrete in each span between the piers, and filling the shearing pockets with non-shrinkage mortar.