Since observation tasks of micro-satellite require rapid multi-target acquisition and high pointing accuracy, the single-gimbal control moment gyro (CMG) is considered as an ideal torque-generating actuator due to its practical performance for the satellite. This paper compares two useful robust attitude control algorithms (sliding mode control method and high order sliding mode control method). These control methods have improved the system's robustness and accuracy. The pseudo-inverse steering logic based on mixed two-norm and least-squares minimisation is chosen in this paper which can deal with both the internal singularity problem and momentum saturation singularities. This attitude control system is verified through numerical simulation. The results demonstrate the validity and feasibility of the proposed approach.