The invention relates to a horizontal negative stiffness device with a vertical damping function. The horizontal negative stiffness device comprises a spherical hinge upper connecting plate, a spherical hinge lower connecting plate, a spherical hinge, an arched spherical face, pre-pressing disc springs, viscous dampers, limiting rods, a bearing base, nuts and inside hexagonal bolts; the spherical hinge upper connecting plate and the spherical hinge lower connecting plate are fixedly connected through the inside hexagonal bolts, and the spherical hinge is embedded into the spherical hinge lower connecting plate for fixation and makes contact with the arched spherical face in a pressure-bearing mode; the upper portions of the pre-pressing disc springs are in welding connection with the arched spherical face, and the lower portions of the pre-pressing disc springs are in welding connection with the bearing base. The viscous dampers are arranged at the internal diameters of the pre-pressing disc springs, the upper portions of the viscous dampers are in welding connection with the arched spherical face, and the lower portions of the viscous dampers are in welding connection with the bearing base. The viscous dampers and the pre-pressing disc springs cooperatively work, and meanwhile negative stiffness and damping force are generated; and the limiting rods are connected with the arched spherical face and the bearing base through the nuts, the pre-pressing states of the disc springs are achieved, and the limiting rods are symmetrically arranged on the two sides of the arched spherical face.