Tracking of non-cooperative maneuver target is the premise of fulfilling complex space task for geostationary-earth-orbit satellite, such as state supervising and maintenance etc. Considering propulsion efficiency, next-generation high-earth-orbit satellites prefer to adopt electric propulsion system. However, the continuous low-thrust characteristics of electric propulsion causes that the classical relative navigation tracking algorithm expectation has some bias, and there is some contradiction between the steady-state performance and the maneuvertracking response for two-stage state estimation method. To solve the rapid-tracking estimation problem of electric-propulsion maneuver target, filtering error theory is adopted to analyze the attenuation factor of the classical algorithm performance, and we obtain the evolvement characteristic of transfer matrix from maneuver acceleration to filtering information. The above evolvement characteristic can be matched by the observation matrix on the basis that detection information of target maneuver can amend the error filter. Then a kind of adaptive variable-dimension two-stage state estimation method is presented, which makes that its performance is equivalent to the classical relative-navigation tracking algorithm in the non-maneuvering interval of target and equivalent to the two-stage state estimation algorithm in the maneuver interval. Meanwhile, it has a faster tracking response. Finally, the simulation results show that for non-cooperative target the steady-state estimation performance of the proposed algorithm is consistent with that of the classical algorithm, i.e. the tracking response is four to five times faster than that of using the traditional method. For tracking of space non-cooperative maneuver target with continuous low-thrust maneuver, the new algorithm is a good exploration.