A novel dual-band miniaturized frequency selective surface adopting fractal elements is proposed. The proposed structure is composed of interconnected four SZ curves of second generation. Such a design is to provide two pass-bands with stable performance, the first band resonates at S-band with a center frequency of 3.02 GHz and the second band is at C-band centered at 7.22 GHz. In addition, the compact structure employing the space filling curve can further reduce the size of the FSS. The dual-band FSS achieves better miniaturization compared with other single layer FSS in previous literature, the dimension of the unit cell is only 0.072λ × 0.072λ, where λ represents the free space wavelength at first resonant frequency. Furthermore, the proposed FSS exhibits great resonance stability for different polarizations and incidence angles. Both the simulation and measurement verify the stable performance of the FSS.