A mathematical model is developed to simulate the dynamics of a flexible cylinder subjected to vortex-induced excitation. The finite element method is used to describe the dynamic characteristics of the cylinder. The fluctuating lift forces induced on the cylinder are assumed to satisfy a modified Van der Pol equation and are determined by the wake-oscillator approach. The dynamic equations of the cylinder are coupled with the modified independent modal space control (MIMSC) method, which actively suppresses the dominant mode of the vibration. The performance of the active controller of the vortex-induced vibrations is obtained at various flow speeds and control weighting parameter. To verify the mathematical model, the computed results are compared with experimental data obtained in a low-speed wind tunnel over a range of Reynolds numbers between 5500 and 7500. Good agreement is observed between the theory and experiments. It was found that the controller is effective in attenuating the transverse vibrations of the cylinder by approximately 40% for all the flow speeds considered.