Abstract：We first introduce the basic theory of the third-order gradient tensor of the gravitational potential, which is also called the gravitational curvature tensor(GCT). Second, we provide analytic expressions of the third-order gradient tensor of the gravitational potential caused by the homogenous spheroid. Finally, through theoretical analysis and synthetic model tests, we discuss the sensitivity of the source’s parameters(mass, buried depth, horizontal location and geometric shape) on the zero, first, second and third-order gradient tensors of the gravitational potential. Results show that, among the zero, first, second and third-order gradient tensors of the gravitational potential, the third-order gradient tensor of the gravitational potential decays most quickly as the distance between observation point and source increases. Therefore, the GCT has multiple characteristics, such as, highest sensitivity on the buried depth of the source; the best exploration capacity for shallow mass, and on the contrary the worst capacity for deep mass; and the highest sensitivity of the horizontal location of the source. This ability is weakened as the buried depth of the source increases. The type is also the most diverse, indicating that under the same distribution of points, the three-step tensor can capture more field and field source information, especially the short-wave component of the gravity field and the remaining mass of the shallow part.