Aiming at the characteristics of non-linearity,uncertainty and susceptibility to disturbance of single-degree-of-freedom magnetic levitation ball system,a back-stepping control method based on extended state observer (ESO-BS) was proposed to improve the control performance of the system.The extended state observer was used to estimate the position,velocity and disturbance information of the levitation ball in real time when the system was disturbed by uncertainty.The estimation was combined with the controller design,then the back-stepping method was used to design the levitation position tracking control law of the magnetic levitation ball,and the Lyapunov method was used to prove the ultimate bounded convergence of the tracking error of the system.The simulation results show that,compared with PID control,the adjusting time of ESO-BS control system is 0.01 s,while that of PID control is 0.08 s,which is obviously longer,so the dynamic characteristic of ESO-BS control is better than that of PID control.When there is uncertainty in the system,the designed control law can realize the stable suspension of the ball,and can realize the position tracking according to the required suspension height position.