Fractal structures has self-similar properties so that they can be applied in the field of frequency selective surface (FSS) as unit cell and the fractal FSS has the nature of simple ,multi-band characteristics on single layer FSS which can be used as spatial pass filters for the incident angle, polarization and the frequency of the electromagnetic wave. Take fractal cross dipole as example, which we can obtain by recursive algorithm and iterative technique, this work gives the expressions of the fractal elements’ geometry and then characterizes the FSS transmission response by the electric field integral equation for the current distribution on the single FSS screen derived from the Floquet's periodic theory unden impedance boundary condition. Genetic algorithm was applied to globally optimize the structure parameters in order to get the design of the double resonant FSS. Finally, FSS sample was prepared by optical lithography and measured in the anechoic chamber. Experimental results show good agreement with the calculations we made for the design of FSS with resonant frequencies 9.2 GHz and 29.4 GHz, which was what we expected from the periodic method of moment.