Nonlinear problem of spatial aeroelastic vibrations of iced conductor, suspended on moving insulator strings is considered. It is assumed that the vibrations occur relative to the initial deflection caused by gravity and wind flow. The conductor tensile strain is determined by quadratic approximation in dependence on its transverse displacements and is considered constant as well. The displacements and angles of twisting of the conductor at its ends as well as the coefficients of the expansions of these functions in sine series with integer number of loops per span are considered as generalized coordinates. The aerodynamic loads acting on the vibrating iced conductor are determined using the conventional quasi-steady formulas for the lift, drag and moment in dependence on the disturbed angle of attack. We obtained general equations of the conductor motion in the generalized coordinates with nonlinear elastic, inertial and aerodynamic forces, and in addition the linearized equations for small aeroelastic vibrations around the static equilibrium position. The latter equations allow determining the critical speed of the conductor flutter. As examples we fulfilled calculations of the critical flutter speed of the conductor with uniform icing. Influence of the non-linearities and some parameters on the conductor behavior was estimated.