We design and fabricate a deformable frequency selective surface (FSS) structure using shape memory alloys (SMA). The unit cell could "remember" two different geometrical shapes and the shapes convert to each other alternately during heating and cooling, that leads to the drift of resonant frequency. Qualitative analysis by equivalent circuit model and accurate numeric calculation are compared to display the character of the transmission. The measurements show that a tuning range of frequency from 13.07GHz to 16.29GHz is achieved when the morphology of the unit cell changes, making the deformable FSS an attractive choice for tunable filter in different frequency bands with the features of wide tuning range and sharp cut-off.