Control of multi-modal structural vibrations has been an important and challenging problem in flexible structural systems. This paper proposes a new vibration control algorithm for multi-modal structural control. The proposed algorithm combines a pole-placement controller with an integral resonant controller. The pole-placement controller is used to achieve a target equivalent modal viscous damping in the system and helps in the suppression of higher modes, which contribute to the vibration response of flexible structures. The integral resonant controller successfully reduces the low frequency vibrations e.g. caused by broad-band turbulent wind excitations. Hence, the proposed hybrid controller can effectively suppress complex multi-modal vibrations in flexible systems. Both numerical and experimental studies have been carried out to demonstrate the effectiveness of the proposed algorithm using a limited number of sensors/actuators.