The galloping models of the iced transmission line based on the conventional cable theory cannot consider the translational and torsional coupling and torsional nonlinearity. According to Hamiton principle and Galerkin method, a 3-DOF galloping curved-beam model of the iced transmission line considering stiffness of insulator strings and adjacent spans as boundary conditions is formulated based on the curved-beam theory. The program code of galloping model based on Curved-beam and cable model developed by Mathematica is used to solve galloping equation of iced transmission line. An example analysis shows that the 3-DOF galloping curved-beam model of the iced transmission line considering elastic boundary conditions is in best agreement with experimental results, which has higher accuracy than the models based on cable theory among all models. With the increase of the boundary spring stiffness, vertical and horizontal displacement amplitudes raise and rotational displacement amplitude diminish accordingly. Both the critical wind velocity and supercritical wind speed for galloping increase. Simultaneously, the range of the wind speed for galloping becomes smaller. The boundary stiffness has a slight effect on horizontal and rotational mode functions and has significant influence on vertical and longitudinal mode functions.