To tackle the galloping issue of ultra-high-voltage transmission lines with large span，a torsional tuned mass damper（TTMD）with eddy current was designed，whose applicability on transmission lines of various spans compared with vertical tunedmass damper was proved. Based on the mechanical model of transmission line with full span，partial differential equations of galloping were derived for the full-span iced conductor-TTMD system. Then the equations were discretized using global shape functions to obtain ordinary differential equation. Subsequently，galloping wind speed was obtained using Lyapunov's stability theorem. An optimization method of anti-galloping using TTMD based on genetic algorithm was established. Considering the uncertainty of declination of ice on conductors，the optimization objective was defined as the minimum galloping wind speed in multiple ice declination angles. Several parameters of TTMD were studied in the optimization process，including frequency ratio，damping ratio，mass ratio，installation position，conductor tension and ice mass. The optimization was performed on 8-bundled conductors of an ultra-high-voltage transmission line with a span of 500 m. The results show that，the TTMD can increase the minimum galloping wind speed with a mass ratio higher than 0.005；the recommended installation position of TTMD lies between the left 1/4 span and the right 1/4 span of the transmission line；the TTMD shows great robustness of control effectiveness；at the design stage of TTMD，the selection of a relatively high conductor tension and low ice mass can lead to safer TTMD design parameters.