Frequency selective surface (FSS) is mainly used as passive filters to separate optical Gaussian beam in quasi-optical system. The multiband FSS on single screen can be designed using self-similar fractal elements as periodic cells. Take cross element for example we can obtain second-order cross fractal element by recursive algorithm. The method of moments is employed to characterize the transmission properties of fractal band-pass FSS combining with Floquet′s periodic theory and boundary conditions. The transmissivity of multiband FSS with resonant frequencies of 58 GHz and 145 GHz are all above 95%. After analyzing the influence of changing the structural parameters of fractal FSS on its transmission characteristic, it is known that the first resonant frequency f1 is decided by the arm length L1 of the original element and the second resonant frequency f2 is sensitive to the arm length L2 of the iterative element, the stability of the transmission characteristics of f1 is better than f2. We examine the stability of the fractal FSS frequency response when changing the incident angle and polarization of the electromagnetic wave.