Using superelastic shape memory alloy (SMA) bars and non-asbestos organic (NAO) friction material, this study developed an innovative self-centering friction damper (SCFD). This hybrid passive control device consists of the self-centering device using SMA bars and the friction energy dissipation device which can provide excellent self-centering ability and energy-absorbing ability to meet the requirements of civil engineering applications. To explore the feasibility and hysteretic properties of the self-centering friction damper, experimental tests under cyclic loading were conducted. According to the experimental results, the proposed SCFD exhibited a stable and repeatable flag-shaped hysteretic response, which can achieve the recovered displacement of 76.07% and dissipated energy of 6.04 kJ at 42 mm. The finite element model of the SCFD using ABAQUS software was established and validated by experimental results. And a series of numerical simulations with different parameters were performed, which enables a more in-depth interpretation of the SCFD. Additionally, a system-level nonlinear time-history analysis was performed on a three-story steel frame equipped with and without SCFDs. The dynamic analysis results indicated that the SCFDs could effectively reduce structural damage and enhance post-earthquake recoverability under rare earthquakes.