In this paper, frequency selective surface (FSS) with low profile, miniaturized structure and closely located dual-band is proposed based on the fractal technology. The FSS is designed by etching the conductive pattern on a single layer substrate. Two fractal slots are designed to increase the spatial efficiency of the pattern and provide two isolated resonances. For the dual-band FSS, the miniaturization should work for both of the resonances to keep the frequency ratio. Therefore, the slots are convoluted as different principles and twisted with each other to keep the miniaturization and isolation. With the thirdorder fractal pattern, two pass-bands are achieved at 1.04 GHz and 1.49 GHz with the frequency ratio of 1.42. The dimension of the element is as compact as 0.039λ × 0.039λ where λ is the wavelength of low frequency resonance. Moreover, benefiting from the miniaturized element, the angular stability is very good that the resonances keep stable when the incident angle increasing from 0° to 60°. In order to get insight of the mechanism of the proposed element, an equivalent circuit model is established and studied. A prototype is fabricated and all the proposed performances are verified by simulations and measurements.