Purpose The purpose of this paper is to equip damping performance of frame structure with viscoelastic dampers connected to supports is studied, the influence of the damper supports and the damping parameters on the damping performance of the structure is analyzed, the practical economical arrangement of viscoelastic dampers on each floor is researched and the calculation method of the seismic effect of the damping structure is presented. Design/methodology/approach In this paper, Fourier transform is applied to the vibration equation of the structure equipped with viscoelastic dampers, the frequency domain solution of the vibration equation is solved and the time-domain solution of the equation is obtained by Fourier inverse transform, from which effects of the support coefficient and the relaxing time coefficient on the seismic response of the structure are analyzed. Findings The seismic effect of each floor and the bottom shear force of each vibration mode of a structure are analyzed, which indicates that the relaxing time coefficient of the damper should be controlled reasonably. Originality/value In this paper, the vibration equation is solved in the frequency domain for frame structure equipped with viscoelastic dampers. The time-domain solution of the equation is obtained by Fourier inverse transform, from which the seismic response of frame structure equipped with viscoelastic damper connected to supports is studied.