This study aimed to develop a novel self-centering friction damper (SC-FD) consisting of the winding rope, the friction shaft and the self-centering spring. The theoretical model and equations for the mechanical properties of the SC-FD were derived. Then, the dynamic performance test of the SC-FD and finite element simulation were done to validate the theoretical mechanical model of the SC-FD. Finally, the influence of the main parameters on the dynamic performance of SC-FD was analyzed and design recommendations were made. The study showed that the SC-FD exhibited stable flag-type hysteretic behavior, with good energy dissipation capability and self-centering performance. The theoretical model and equations derived in this study can be used to predicate the behavior of the SC-FD accurately. The parameters, such as the initial inclination angle of the winding rope, winding turns of the winding rope and the stiffness of the self-centering spring and so on, had significant influences on the mechanical performance of SC-FD, which should be optimized in the designing of the SC-FD in order to get excellent mechanical performance.