A bandpass frequency selective surface (FSS) with fourth-order bandpass filtering response is proposed based on aperture-coupled patch resonators (ACPRs) under the operation of TM and TM resonant modes. An initial bandpass ACPRs FSS with second-order filtering response is firstly realised by periodically arranging the back-to-back patch resonators with coupling apertures etched on the common ground. In order to combine the resonant modes TM and TM for a higher-order filtering response, seven pairs of shorting pins are properly loaded based on the cavity model theory for the microstrip patch resonator. The loaded shorting pins make the TM mode of the ACPRs shift towards the higher frequency, while the TM mode keeps nearly unchanged. As a result, these two resonant modes can be allocated in proximity to each other to finally realise a fourth-order bandpass filtering response. To validate the design concept, an FSS prototype is designed and fabricated. Reasonable agreement between the measured and simulated results validates the conceptual design.