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The vibration of the conductor suffered an excitation is studied in this paper.The nonlinear motion equation of the conductor is constructed by using Hamilton theory.After one order Galerkin discretizing, the averaging equations and the frequency-response are obtained by multiple scale method.After six order Galerkin discretizing.the numerical results are obtained.To study the effect of the damper to the vibration of the conductor.a damper is suspended on the conductor at x2.Similarly.the nonlinear motion equations of the conductor with a damper are constructed.The averaging equations are also obtained for one order Galerkin discrete system, and the effects of the parameters of the damper to the conductor are discussed.Additionally, the numerical results are obtained for the six order Galerkin discrete system.After comparing, the amplitude of the conductor with a damper is seriously decreased.