Owing to the superior mechanical performance and material efficiency, the combination of prestressed concrete (PC) slabs and corrugated steel webs (CSW) as PC girder with CSWs (PCGCSW) is extensively applied to railway and highway bridges. To overcome the shortcomings of traditional balanced cantilever construction (TBCC) of PCGCSW, reduce environmental impact, and promote sustainable construction, a novel asynchronous-pouring-construction (APC) technology is introduced in this paper. This improved method makes full use of the excellent shear capacity of the corrugated steel webs (CSWs) to support the hanging basket, increases the construction platforms to accelerate the construction speed. Based on a practical project of a long-span composite box girder bridge with CSWs in China, the construction process of the APC method is systematically introduced, and the structural safety and environmental sustainability of such bridge using APC technology are evaluated and compared with that using TBCC. The comparison results indicate that APC method can reduce the compressive stress of top concrete slab, but slightly increase the shear stress and deflection during the cantilever construction stage because the hanging basket is directly supported by CSWs. Besides, the weight of the improved handing basket in APC technology is reduced up to half in comparison that in TBCC. Accordingly, the APC technology saves a lot of energy consumption, reduces huge CO2 emissions for construction equipment, and shorts construction period. Therefore, the utilization of APRC technology can ensure the bridge’s safety and reliability, effectively accelerate construction speed, reduce the construction load, decrease the environmental pollution, and save the engineering cost, which can be regarded as a sustainable and environmental-friendly construction method for composite bridges with CSWs.