In this study, the wind response characteristics of a transmission tower are investigated through stochastic analysis considering the dynamics of a transmission line, The assemblage of the transmission line and insulator are modeled as a double pendulum system connected to the SDOF model of the tower. It is observed that the background component of the overturing moment induced by the wind response of the transmission line has considerable portion in the total overtuming moment. Based on this observation, a rotational viscoelastic damper is proposed for the suppression of the transmission line response to reduce wind load on the transmission tower. To verify the effectiveness of the proposed damper, time history analysis is conducted for various wind velocities. From the result of the analysis, the proposed damper is proved to be effective in the reduction of the background component rather than the resonance component of the support reaction of the transmission line.