The purpose of this paper is to simulate the vibrations caused by the aerodynamic force of the wind blowing. Disturbances of air currents over the cable cause the oscillations of the cable with certain amplitude. In this paper, the Dryden turbulence model is used to model wind-induced aerodynamic force. The equations of motion of the cable connected to the electromagnetic damper is obtained by using the Hamilton principle and then they are discretized to a set of linear ordinary differential equations by adopting the Galerkin method. In the following, the transfer functions of the first vibration mode of the cable are obtained and the bode diagrams for these transfer functions are plotted using MATLAB software. Then the effects of random gust parameters, such as length scale, turbulence intensity and wind speed on the frequency response of the cable are investigated. The results show that increasing length scale and wind speed decrease the resonant frequency of the system.