Abstract: Disclosed is a steel-concrete composite beam. The steel-concrete composite beam has an asymmetric I-section steel member having an upper flange, a lower flange and a web. The web is formed with at least one opening at a predetermined interval. The upper flange has a narrower width than the lower flange. A pair of C-section steel members is attached integrally to the lower flange of the asymmetric I-section steel form a first space filled with concrete. The concrete interlocks with the lower flange. A deck is supported on the C-section steel members. At least one transverse reinforcing bar of slab is arranged through the opening perpendicular to the asymmetric I-section steel. An upper concrete slab is poured with the concrete to be formed at a predetermined thickness. The concrete fills in a second space defined by the C-section steel members and the lower flange so that the upper flange of the asymmetric I-section steel is embedded.