The continuous curved box girder with corrugated steel webs is extremely complicated due to the coupling effect of bending and torsion. In order to study the mechanical properties of continuous curved box girder with corrugated steel webs, considering the effect of bending-torsion coupling, shear lag and shear deformation, based on previous research results, the restrained torsion differential equation of simply supported statically indeterminate curved box girder with corrugated steel webs (CCBG(CSWs)) are derived based on the energy method, using the differential equation combined with the three-bending moment method to solve the internal force of a three-span continuous curved box girder with corrugated steel webs, and the results are compared with those of the curved bar structure mechanics method and of the finite element analysis. The results show that: considering the effect of bending-torsion coupling, shear lag and shear deformation, the internal force results obtained by the method proposed in this paper are in good agreement with the results of finite element calculation, which verifies the correctness of the method proposed in this paper. Under the same load, the internal force of the continuous curved box girder with corrugated steel webs is very close to the internal force of the traditional concrete continuous curved box girder, indicating that the continuous curved box girder webs material has a relatively small influence on the internal force of the bridge span.