A new hysteretic nonlinear model of quad iced bundle conductors is constructed. The bifurcation equation is obtained by applying the undetermined fundamental frequency method of the complex normal form. The transition set and bifurcation diagrams for the singularity are presented. Then the corresponding relations between the unfolding parameters and the system parameters are given, and the sensitivity parameters and its range of values are obtained to analyze and to control the galloping of the quad iced bundle conductor.