Reaction wheels are widely used for spacecraft attitude control in missions that require fine pointing accuracy and stabilization nowadays. But the friction produced by the reaction wheel assembly (RWA) itself when crossing zero is one of the most significant sources of disturbance. And it is necessary to eliminate these disturbances, especially for those cases that the wheels are running at low-speed throughout the space mission. The mathematical model of the reaction wheel assembly driven by a DC motor is presented on the base of Dahl friction equations. And a state observer is constructed to estimate the friction torque in order to compensate for it. A numerical simulation model, which assumes the satellite attitude is controlled by three reaction wheels arranged in an orthogonal geometry, is established. The simulation results prove that this method can improve the satellite attitude pointing accuracy and stability efficiently. Finally, the integration of the observer method and a sliding-mode control law is discussed.