In this paper, a method of designing the frequency selective structure based on spoof surface plasmon polariton (SSPP) is proposed and demonstrated. According to the applications in different working bands, the designed frequency selective surface (FSS) and metallic fishbone structure array can be combined together to form a new frequency selective structure and satisfy the requirements for practical applications. Meanwhile, a dual-band-pass frequency selective structure with the property of steep cut-off frequency and high-efficiency transmission and inhibition is designed by using this method. The dual-band-pass frequency selective structure is composed of a metallic fishbone structure array and two identical FSSs. The metallic fishbone structure based on SSPP coupling can form a broadband high-efficiency transmission below the cut-off frequency of SSPP on the metallic fishbone structure. When a dual-band-pass FSS is loaded to this metallic fishbone structure array, a dual-band-pass frequency selective structure can be achieved. To improve the impedance matching of the dual-band-pass frequency selective structure, two identical FSSs are respectively loaded to the top and bottom sides of the metallic fishbone structure array. The simulated transmissivities of the dual-band-pass frequency selective structure exceed-0.5 dB in two frequency ranges:3.0-4.1 GHz and 10.5-10.9 GHz. The simulated transmissivities are lower than-10 dB in other frequency ranges:4.7-9.2 GHz and 12.1-18 GHz. The simulated transmissivities are even below-20 dB from 12.4 GHz to 15.5 GHz. The electromagnetic waves can be efficiently transmitted in the passband and restrained in the stopband. Then the dual-band-pass frequency selective structure is fabricated by using the printed circuit board technique and measured in the anechoic chamber. The measured results indicate that the real property of the dual-band-pass frequency selective structure is consistent with the simulated property and this method of designing the frequency selective structure is feasible. After filling the lightweight foam into the gap of the metallic fishbone structure, the mechanical loading property can be highly improved. Therefore, we can realize the design of combined structural and functional performance.