The viscoelastic damper is one of the most promising devices for vibration mitigation. In order to reduce dynamic responses of iced transmission lines due to strong wind, a new kind of viscoelastic antigalloping device (VEAGD) is developed. Experimental and theoretical studies indicate that the device has fine energy dissipation capacity and high damping characteristic. Then, the motion equations of the iced quad-bundle transmission lines incorporated with VEAGDs are established by employing Lagrange equation based on the assumed mode method. At the same time, the parameters and positions of the VEAGDs are determined optimally by the genetic algorithm. Numerical analysis results show that VEAGDs have excellent antigalloping effect, and the dynamic responses of the transmission lines with optimally designed VEAGDs are mitigated more effectively.