A hybrid frequency selective rasorber is presented in this letter based on hybrid lossy layers. The hybrid lossy layers is composed of an absorption-transmission (A-T) layer and a transmission-absorption (T-A) layer, which are responsible for the absorption performance in the low and high frequency respectively. The A-T layer is composed of a lumped-resistors loaded cross-frame structure (CFS), which connects four parallel inductor and capacitor resonators. The T-A layer is constructed by a parallel plate capacitor loaded square loop resonator connecting four lumped-resistor loaded T-shaped metal branches. The frequency selective surface layer is composed of metal square slot. The hybrid frequency selective rasorber provides a transmission window around 10 GHz and two-sided absorption bands in 3.19—9 GHz and 11.85–21.18 GHz, meanwhile the wideband reflection suppression (S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> <−10 dB) is achieved from 3.2 to 21.18 GHz (147%). An assembled prototype is measured to verify the simulated results.