The stability of long span steel arch structure of globe transportation center (GTC) in the Beijing Capital International Airport was studied. Different objective models such as single arch model, composite arch model and global structural model were introduced to analyze the structural stability by means of the finite element technique.The eigen buckling factor of the steel arch structure was analyzed. The geometrical nonlinearity, elastic-plastic nonlinearity and initial imperfection were taken into account in the investigation of the structural buckling, and the nonlinearity reduction factors for the steel arch structure were discussed. The effects of geometrical nonlinearity and initial imperfection on the structural buckling are light while the effect of material nonlinearity is quite remarkable. For a single steel arch, the dominant buckling mode occurs in out-of-plane of arch structure. The out-of-plane buckling factor of the composite steel arch is greater than that of the single steel arch while the in-plane buckling factor of the former is somewhat less than that of the latter. Moreover, the webs near the steel arch feet have the lowest local buckling level and the local buckling is more serious than the global buckling for the global structure.