This paper proposes a systematic design method for dual-passband microstrip bandpass filters composed of stepped impedance resonators (SIRs) with suppression of higher order spurious responses. A specific dual-band fractional bandwidth design graph must be built. The line widths of the SIR and the gap size between SIRs provide two freedoms for determining the realizable fractional bandwidth of the two passbands. The inherent transmission zeros of coupled SIRs are used to suppress the unwanted spurious responses. A complete design procedure considering both the synthesis of passband responses and the suppression of spurious responses is detailed depicted in this paper. The idea is verified by a fabricated experimental filter. The measured frequency responses shows that the spurious response can be suppressed below -35.4 dB and the upper band can be extended to 5.62 f0 (13.77GHz).