A scan loop model for a spin-stabilised seeker is introduced, which includes gyro-dynamics with direct-and cross-spring constants for considering the autoerection effect of the gyro. The LQG/LTR and H-infinity controllers are designed for the seeker scan loop system which has model uncertainty and is subject to external disturbances. The performance of LQG/LTR controller call be improved by obtaining uniform singular values over all frequencies for the target feedback loop. The H-infinity controller is designed in the framework of the standard H-infinity optimisation problem with model matching. The proposed H-infinity method can reflect not only frequency domain specifications but also time domain ones, such as transient response characteristics and multivariable interaction between output channels, differently from the mixed sensitivity problem. It is shown that the designed LQG/LTR and H-infinity controllers offer good performance and robustness properties, and both controllers are very effective in the seeker scan loop system.