An Iterative Learning Control (ILC) method with Extended State Observer (ESO) is proposed to enhance the tracking precision of telescope. Telescope systems usually suffer some uncertain nonlinear disturbances, such as nonlinear friction and unknown disturbances. Thereby, to ensure the tracking precision, the ESO which can estimate system states (including parts of uncertain nonlinear disturbances) is introduced. The nonlinear system is converted to an approximate linear system by making use of the ESO. Besides, to make further improvement on the tracking precision, we make use of the ILC method which can find an ideal control signal by the process of iterative learning. Furthermore, this control method theoretically guarantees a prescribed tracking performance and final tracking accuracy. Finally, a few comparative experimental results show that the proposed control method has excellent performance for reducing the tracking error of telescope system.