In this paper, an optimal active controller is designed to prevent the shimmy vibrations in aircraft nose landing gear. The controller is designed according to the linearized system while the input is implemented on the real non-linear plant. Shimmy vibration is the lateral and torsional vibrations in the wheel that causes instability in high speed performances. Thus, control and suppressing of this vibration is extremely important. In this paper, using the nonlinear dynamics of the nose landing gear system, the equivalent linearized system is extracted and then its related linearized state space is derived. Stability, controllability and observability of the system are investigated based on the linearized model of the system and damping the shimmy vibrations is performed with the least consumption of energy using Linear Quadratic Regulator (LQR). To estimate the states of the system which are not measurable using ordinary sensors, an observer is designed and implemented using separation principal. To verify the performance of the proposed controller, vibration response of the open loop system is compared with the closed loop response of the designed optimal controller. Considerable improvement can be seen in the performance of the closed loop system since not only the vibrations are effectively damped but also the consumption of energy is minimized. Finally, digital control system is extended in order to implement the proposed controller on the discretized model of the system and the effect of sampling rate on the accuracy of the system is studied.