The invention belongs to the technical field of materials and antenna covers, and particularly relates to a full-polarization flexible frequency selective surface structure for inhibiting a parasiticpassband and an antenna cover. The structure comprises a dielectric substrate which is made of a non-conductive material, and periodic metal foil layers which are attached to the upper surface and thelower surface of the dielectric substrate respectively. The full-polarization flexible frequency selective surface structure is virtually divided into a plurality of periodically-arranged square unitstructures. Each square unit structure comprises a dielectric substrate unit, a first metal micro unit attached to the upper surface of the medium substrate unit and a second metal micro unit attached to the lower surface of the medium substrate unit. The antenna cover is used for covering the radiation direction of an antenna system and is composed of the full-polarization flexible frequency selective surface structure. The antenna can keep good radiation characteristics in the frequency band of the K-band from 22.3 GHz to 25.3 GHz, and a good out-of-band rejection performance is achieved outside the passband.