Abstract: The random vibration theory is used to solve the mean square deviation of the displacement regularization coordinate of the frame structure with high-efficiency energy-consuming friction dampers under small earthquake action. The influence of friction damping force on the mean square deviation of the displacement regularization coordinate of the above frame structures under improved Kanai-Tajimi power spectrum of seismic excitation is studied; The conditions for starting energy consumption of friction dampers are analyzed; The article also studies the equivalent damping ratio of the frame structure with high-efficiency energy-consuming friction dampers. On this basis, the damping effect of the frame structure with high-efficiency energy-consuming friction dampers on giant earthquakes is studied.