A Stewart platform is a well-known mechanism which can be used for a wide variety of vibration control problems. In this paper, an LQR controller for a Stewart platform prototype is proposed which, combined with a proportional derivative gain matrix, achieves a good performance when compared with the classical PID control system. By testing some trajectories, we observe that the tracking error between the actual and pre-established trajectories is smaller by applying the controller supplied in this work. The final purpose will be the implementation of this kind of control in a real Stewart platform constructed at the Universitat Politècnica de Catalunya (UPC) by our research group.