Proposed in this study is a type of friction damper characterized a continuously variable post-sliding stiffness, which provides an increasing post-sliding force with the accretion of the deformation. It is possible to adjust the output force according to the performance targets at different earthquake levels, thus enlightening a practical approach to the explicit structure control to satisfy all of the required performance objectives. Theoretical analyses reveal that the parabola shape of the sliding surface would introduce a cubic force-displacement relationship, which was also demonstrated by sophisticated finite element models. The typical mechanic model was then incorporated into the source code of OpenSEES. The dynamic analysis gave reasonable results and experimental results also demonstrated that the proposed friction damper is able to reduce the displacement response and more important, is helpful to prevent a structure from collapse.