A stiffness-controllable earthquake-isolation support using negative gravity stiffness, which comprises an upper plate connected to an upper structure, a lower plate connected to a base structure at the bottom, K supporting columns arranged longitudinally between the upper and lower plates, with the supporting columns respectively connected with the upper and lower plates through a ball hinge, and L elastic connecting plates arranged laterally between the supporting columns, wherein K≧3, L≧N×K and N≧1. The earthquake-isolation support, the supporting column and the ball hinges at both ends of the supporting column form, under the action of gravity of the upper structure, the negative gravity stiffness that causes the upper structure to deviate from the equilibrium position, and the frame structure restores the upper structure to the equilibrium position, with the stiffness of the earthquake-isolation support adjustable.