A revised moment-rotation relationship of friction damped self-centering connection was improved and the design idea of friction damped self-centering connection was put forward to meet the design targets of different seismic performance of modern building structures. The finite element software ABAQUS was used to design 5 specimens of composite frame with friction damped self-centering connection and simulate their seismic performance under cyclic loading. Based on the simulation data, the axial compression, the dimension of the slotted hole, the boundary condition at PEC column bottom and the bolt layout of T-stub were taken into consideration to obtain influence mechanisms of these factors on the seismic performance of specimens, including the hysteresis performance, lateral stiffness degradation, residual deformation, and energy dissipation capacity. The results demonstrate that the bearing capacity and lateral stiffness of PEC column meet the requirements of the vertical members for the self-centering structures and the dimension of the slotted hole can be flexibly designed to control the developing process of friction slip energy dissipation and bearing-type force-transferring mode, to meet different seismic performance design targets. Meanwhile, the layout of high strength penetrating bolts in practice can soundly play the self-centering function and friction energy dissipation capacity of partial self-centering connection. The connection type of the PEC column bottom has meaningful effect on the loading-deformation and the stiffness distribution of the frame, while the second-order effect of the axial compression just has adverse impact on the self-centering function and bearing capacity.