A robust stabilization design method based on linear active disturbance rejection control(ADRC) with immune optimization is proposed for a planar Acrobot affected by uncertainties such that the end point of the robot can reach and be stabilized at the target position from any initial position. Firstly, the relationship between the position of the end point of the robot and the angle of the actuated joint is obtained by means of the state constraint relationship between the angle of the actuated joint and the angle of the underactuated joint. After that, the position control of the end point is converted to the angle control of the actuated joint. Secondly, in order to shorten the motion path, a condition of minimum angular displacement restriction is defined, and an immune algorithm is designed to obtain the minimum desired angle of the actuated joint corresponding to the target position. Thirdly, the linear ADRC control technique is introduced, and the uncertainties such as model uncertainties and unknown disturbances are regarded as an extended state of the system. A linear extended state observer and a feedback controller based on state error are designed to realize the robust stabilization of the Acrobot when only the angle of the actuated joint is measurable. Finally, simulations are conducted to show that the proposed method has better robust control performance.