Abstract This paper proposes a novel shape memory alloy (SMA)-friction damper (SFD) which is composed of friction and SMA energy consumption in parallel. Experiments are carried out to demonstrate the effects of the loading frequency, displacement amplitude and number of SMA wires on the hysteretic behavior of the SFD. Experimental results show that the effect of the loading frequency can be negligible, while the energy consumption increases almost linearly with the displacement amplitude. The increment of the number of SMA wires can significantly increase the stiffness and self-centering capacity to improve the performance of the SFD. Then, a numerical model of the SFD is established by the connector and solid elements in ABAQUS. Finally, a beam string structure, a suspend dome structure, K6 and square-pyramid double-layer spherical reticulated shells with and without SFDs under nine ground motions are analyzed by nonlinear dynamic analysis. For the controlled cable supported structures, the reduction ratio of the peak acceleration and peak displacement reach 46.47% and 52.61%, respectively. And for the controlled double-layer spherical reticulated shells, the reduction ratio of the peak acceleration and peak displacement reach 59.95% and 42.94%, respectively.