Abstract: To solve the problem that energy dissipation and damping technology needs to arrange energy dissipation devices in multiple floors to achieve the ideal damping effect, a linear hysteretic damping model with negative stiffness characteristic was proposed in this paper, which was arranged at the bottom of the structure. By the contribution of the negative stiffness, the mechanical isolation layer was formed to reduce the seismic action, and the displacement of the equivalent isolation layer was controlled by the energy consumption mechanism. Based on the stationary random response analysis of single degree of freedom (SDOF) system and seismic time history response analysis, it is verified that the negative stiffness linear hysteretic damping can reduce the acceleration and displacement response of the structure. The shock absorption analysis of a real thermal power plant structure shows that the negative stiffness linear hysteretic damping can extend the period of the structure, improve the damping ratio of the structure, and play a significant role of control effect on the seismic response of the structure.