Frequency-selective surfaces (FSSs) are widely employed in antenna's radar cross-sectional reduction, which plays a key role in improving survivability and penetration ability of future military systems. In practical, dual-band bandpass FSSs with large band ratio (BR) are urgently needed for some military equipment, such as homing head, that can detect both middle and far range targets. In this paper, a novel method for designing dual-band bandpass FSS with large BR is proposed. The method can provide a large BR response, by utilizing a spurious-free structure and combing resonant and nonresonant elements. The detailed analysis is presented with the aid of equivalent circuit model as well as closed-form equations to reveal the operating mechanism. A design example is simulated, fabricated, and then measured. Two excellent passbands are obtained with a large BR value of 15.3 in experiment. Moreover, a −10 dB fractional bandwidth of 164.3% is realized from 1.31 to 13.35 GHz, without observing any spurious transmission windows. In conclusion, our proposed method fills the gap of the existing dual-band FSSs to obtain a large BR value of more than 6 and could be a good guidance for designing the future multiband FSSs.