In order to make the dual-band frequency-selective surface (FSS) used in the engineering conditions of thick substrate, wide band spacing and large incident angle, an FSS structure with dual-band at Ku-band and Ka-band is presented. The stable filtering condition of the FSS is analyzed by using the grating lobe diagram, and the transmission of the FSS with combination or fractal elements is calculated using the vector modal matching method. The design method of the dual-band FSS with thick substrate is obtained by analyzing the resonance mode of the element and the transmission of the FSS. By using those methods, an FSS with combination elements of the square and Y loops is designed. The simulated and tested results show that the dual-bands of the structure at Ku-band and Ka-band are stable and the transmissions of the two pass-bands are larger than 75% when the incident angle is varied from normal to 45. This paper provides some theoretical and experimental references for the design of the dual-band FSS with thick substrate, wide band spacing and large incident angle.