Atom-interferometry gravity gradiometry has been developed as a promising technique for future gravity gradiometric missions after GOCE due to its greater sensitivity in micro-gravity environments and constant performance over the measurement bandwidth. In this paper, a feasible method of spaceborne atom-interferometry gravity gradiometry is proposed by utilizing the free-fall condition of the cold atoms in space. Compared with GOCE, which shows an in-orbit noise performance of 10~20 mE/Hz^1/2, the scheme described in this paper would achieve a high sensitivity of 1.9 mE/Hz^1/2 for gravity gradients measurement by reducing the orbital altitude and optimizing the interrogation time for atom interferometry. The results show that the proposed scheme could significantly augment the spectral content of the gravity field in the degree and order of 280~316 and resolve the global gravity field with an improved accuracy of 0.2 cm@100 km and 0.85 cm@80 km in terms of geoid height, and 0.06 mGal@100 km and 0.3 mGal@80 km in terms of gravity anomaly after 1270 days of data collection.