The present invention is to provide a continuous composite steel girder bridge using an apparatus to provide a temperature gradient to the steel girder (2) by circulation hot water. The apparatus is comprised of: a hot water circulation pipe (11) attached to steel girder (2) for providing hot water circulation before the composition of the steel girder (2) and the concrete slab (1) starts and until such a composition is completed; a temperature control sensor (12), attached to the steel girder (2) for sensing the temperature of the steel girder (2); and a controller (13) for controlling the temperature of the steel girder (2) to retain a predetermined temperature gradient while the composition effect takes place.