This paper presents a novel frequency selective surface with good transmissive property at high frequency and wideband absorption over lower band. The absorptive frequency selective surface structure is composed of a lossy layer and a bandpass layer. The analysis by the equivalent circuit method shows that the lossy layer should generate parallel resonance in the passband, so the specific equivalent circuit model is given and verified in Advanced Design System. In the design of the lossy layer, two lumped resistors are loaded into the metallic cross-type patch to divide it into two parts for parallel resonance. The bandpass layer is implemented using a lossless slot-type Frequency Selective Surface. The simulation results show that an insertion loss of 0.7 dB can be obtained at 12.75 GHz, and a wide absorption band from 4.8 GHz to 11.2 GHz is realized. A prototype was fabricated and tested, and the experimental results are in good agreement with the simulation results.