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The thickness of the Antarctic ice sheet is a crucial parameter for inferring glacier mass and its evolution process. In the literature, the gravity method has been proven to be one of the effective means for estimating ice sheet thickness. And it is a preferred approach when direct measurements are not available. However, few gravity inversion methods are valid in rugged terrain areas with undulating observation surfaces (UOSs). To solve this problem, this paper proposes an improved high-precision 3D density interface inversion method considering terrain and UOSs simultaneously. The proposed method utilizes airborne gravity data at their flight altitudes, instead of the continued data yield from the unstable downward continuation procedure. In addition, based on the undulating right rectangular prism model, the large reliefs of the terrain are included in the iterative inversion. The proposed method is verified on two synthetic examples and is successfully applied to real data in East Antarctica. [ABSTRACT FROM AUTHOR]