It is recognized that unstable vibration occurs at a rotating speed above the major critical speed by a rotating-conducting-disk type magnetic damper, but not by a rotating-circular-magnet type magnetic damper. In addition, magnetic dampers generally have relatively poor damping performance. In the present work, two new rotating-circular-magnet type magnetic dampers, (which consist of a combined hollow cylinder magnet with alternating directional magnetic poles), are introduced and their design method is presented. Applying the modeling method that the authors have been studying, a prototype magnetic damper with a combined magnet is fabricated and the damping ratios from the analytical results agree well with those from the experimental results. Rotating tests are performed and it is confirmed that unstable vibration does not occur at a rotating speed of more than twice the major critical speed. Based on these findings, an optimally designed magnetic damper with a combined magnet is developed and a damping ratio of 0.25 (damping coefficient of 215 Ns/m) is achieved.