The problem of any selected position hovering control of uncontrolled tumbling satellite was researched. A three-dimensional relative motion equation of arbitrary eccentricity was established in the target orbital coordinate system, and the attitude motion characteristics of the uncontrolled tumbling satellite were analyzed. The hovering problem was decoupled into two-dimensional fuzzy control problem of three channels, and the Mamdani fuzzy controller was designed with the channel x as an example. Determining the corresponding fuzzy subset, membership function and fuzzy control rule table, the fuzzy was solved by using the area center method. The control performance of the designed fuzzy controller was verified by numerical simulations.