Since the damper is widely used nowadays, traditional friction dampers with no self centering function cannot adapt to different vibration intensities and will be seriously damaged after the earthquake. In this paper, a new type of self centering variable friction damper is proposed based on the superelasticity of shape memory alloy. The structure and basic working principle of the damper were introduced, and its mechanical model was then established. Through the mechanical test of the damper, the following conclusions are obtained: (1) The damper can not only meet the requirements of energy dissipation under different earthquake intensities but also has a good self centering ability. (2) The hysteretic curve obtained from the mechanical experiment is in good agreement with the derived mechanical model, which confirms the correctness of the model. (3) The energy dissipation capacity of the damper increases with the increase in the diameter of alloy wire, bolt preload, and slope gradient. The residual displacement decreases with the increase in the diameter of alloy wire and slope but increases with the increase in bolt preload.