This paper concerns with vibration suppression control for three inertia resonance system which can be used as the model for many moving mechanisms widely used in industry such as steel rolling mills, flexible arms, large-scale space structures, etc. Since the mechanical resonance which causes vibration is unavoidable, especially at high speed operation, vibration suppression plays a key role in improving the accuracy of the system. In this research, a linear quadratic regulator-based speed controller with an integrator that can effectively suppress the torsional vibration is applied to control the system. Instead of using conventional state observer that is sensitive to noise and model uncertainties, the extended state observer is used to overcome the disturbance and uncertainty problems. Moreover, this observer also gives us the load torque information that is used to improve the load response. Simulation results show the effectiveness of the proposed controller. In addition, the comparison to conventional PID controller also be done to verify the advantages of the proposed approach.