The interest in space-related activities has grown recently on a global scale. The determination and control of attitude are necessary all space duties. As it affects the satellites mission accuracy, many researches are related to it. Attitude control systems (ACS) design and modelling are represented in this paper. The mathematical models for CubeSat and reaction wheels that act as actuator and the proposed optimal control system are introduced. The proposed controller is applied to control and stabilize the CubeSat through a set of reaction wheels. The simulation results show the superior results of the proposed controller compared with traditional control systems in the presence of external disturbances and white noise. The withdraws of each control system are presented through the simulation results. The main contribution in this paper is solving the attitude control problem for a CubeSat using LQR approach in the presences of disturbances and noise.