Experimental and numerical study on the mechanical performance of curved steel–concrete composite box girders is reported in this research. First, this research establishes a theoretical model for curved composite girders with 11° of freedoms (DOFs) for each node. The DOFs include the longitudinal displacement, transverse displacement, deflection, torsion angle, warping angle, and interface biaxial slip between steel and concrete. Based on the virtual work theorem, the equilibrium function, the stiffness matrix, the node displacement matrix and the external load matrix are proposed for the curved composite girders using the FE spatial discretization. Second, the authors conduct an experimental program on three large-scale curved composite girders with various interface shear connectors and central angles. The comparison between the developed finite beam element, the elaborate FE model and the test results indicates the developed finite beam element has an adequate level of accuracy in predicting the deflection, the torsion angle and the axial strain distribution of test specimens. Third, based on the developed finite beam element model, the effect of initial curvature, number of diaphragms, and the interface connector stiffness on the curved composite girder is examined. The simulation results showed that the initial curvature significantly contributes to the displacement and stress of composite girders. Applying more diaphragms can notably reduce the distortion angle and distortion displacement. The interface shear connector stiffness has a significant influence on the curved composite girder. With the increasing shear connector stiffness, the displacement and stress of curved composite girders decrease notably. Based on the parametric analyses, it is recommended to limit the central angle of simply supported composite girder below 45°, to apply an adequate number of diaphragms, and to design curved composite girders as fully shear connection specimens.