Abstract: A semi-active adaptive control algorithm for closed-loop cable vibration control with magnetorheological (MR) dampers is developed based on measurement displacement. A geometrical nonlinear finite element formulation is employed for analyzing the dynamic responses of the cable-MR dampers system in time domain. The performance of the proposed semi-active control algorithm with MR dampers is compared with that of the passive control algorithm by using MR dampers or oil dampers optimally tuned to the first three modes. The numerical simulation results show that the initial value of parameters of adaptive control algorithm does not influence their final optimization results. The semi-active control is superior to the optimum passive control tuned to a particular mode.