The slant-axis telescope has a novel structure and its unique structural design is more suitable for extreme environment such as the South Pole. However, there is a lack of research on the dynamic modeling and the controller design of slant-axis telescopes at home and abroad. Firstly, the dynamical analysis of the slant-axis telescope is carried out. The 2-degree-of-freedom rigid body model of the telescope is established by the Lagrange method. Next, combining the flexibility of the driver system and disturbance, a mathematical model of the rigid-flexible coupling system of the slant-axis telescope is completed. Then, according to the mathematical model, a sliding mode controller based on the disturbance observer is designed to suppress the disturbance and realize the robust control of the slant-axis telescope. Finally, the simulation results show that the disturbance observer based sliding mode controller gets better dynamic performance and anti-disturbance characteristics than the traditional Proportion-Integration-Differentiation (PID) controller in the case of considering nonlinear external interference of the model.