To provide a more reliable rotor damping system for high-speed compressor with flexible rotor, a passive magnetic damping integrated with an active axial bearing (PMDAB) system is proposed. The PMDAB system can provide active force in axial direction and also can provide damping force without control system in radial direction. To enhance the damping ability of the system, an analytical model is set up especially for the high-speed vibration rotor, and the relation between resistance of radial coils and the provided damping force is discussed for the first time. The coupling characteristic between passive radial damping coefficient and active axial bearing stiffness is also analyzed; the result shows that the coupling is too small, therefore can be neglected. Finally, a design example for a high-speed compressor is given based on electromagnetic analysis of PMDAB and dynamic analysis of the flexible rotor. The analytical and design results, which are verified by the finite element method result, show that the PMDAB is effective in controlling the first bending vibration of flexible rotor.