The fractal elements were exploited to design single layer Frequency Selective Surfaces (FSSs) as multi-band pass filters to meet the multi-band and integration requirements of the communication apparatus.Firstly, the geometry expression of a Y aperture fractal FSS with a symmetry structure and anti-cross polarization was proposed by recursion and iterative operations. Then, combined with Floquet theory and the full-wave periodic method of moment,an electric field integral equation to describe the current distribution of the FSS surface was obtained to quantitatively analyze the frequency response of the lattice and structural parameters of Y aperture fractal FSS, such as pole length, aperture width,and the different polarizations of incident electromagnetic wave. Finally,a FSS sample was achieved by the photolithography technology and experiments in the anechoic chamber. Experimental results show that the estimation empirical constant κ is 0.79 for designing the resonant frequencies of FSS and the bandwidth expands to 650 MHz when the width of aperture varies from 1.0 mm to 1.5 mm.Moreover, the effects of incident angle is highly sensitive to the lattice of the periodic unit cell. Obtained results are well coincident with that of theoretical calculation,which means the single-layer fractal FSS with multiband characteristics can satisfy the engineering requirements after parameter optimization.