A tip-tilt mirror (TTM) control method is designed to enhance the control bandwidth and ensure the rejection performance of the adaptive optics (AO) tip-tilt correction system. Optimized with the Smith predictor and filter, linear active disturbance rejection (LADRC) is adopted to achieve the tip-tilt correction. An AO tip-tilt correction experimental platform was built to validate the method. Experimental results show that the proposed method improves the control bandwidth of the system by at least 3.6 times compared with proportional–integral (PI) control. In addition, under the same control bandwidth condition, compared with the Smith predictor and proportional–integral (PI–Smith) control method, the system is more capable of rejecting internal and external disturbances, and its dynamic response performance is improved by more than 29%.