Abstract: The dynamic behavior of an ice-covered cable is complicated because of the eccentricity over the cable’s cross-section, which makes the in-plane and out-of-plane vibrations coupled with the torsion vibration. A three-dimensional coupling model of a suspension cable loaded by wind excitation is developed, with the wind force expressed as a nonlinear function of the angle of attack. The governing partial differential equation of motion is derived through the Hamilton’s principle and discretized using the Galerkin approach. The stability region in the parametric space of the cable’s equilibrium configuration is obtained using Routh-Hurwitz criterion. The critical wind speed of the Hopf bifurcation is determined and later verified numerically. The boundary shape of the stability region is obtained through an approximately analytical method in the vicinity of a given Hopf bifurcation point, by which a fair amount of computational cost is saved.