For potential military applications, a flexible metamaterial absorber (MMA) working on whole K-bands with total-thickness of 3.367 mm, ultra-broadband, polarization-insensitive, and wide-angle stability is presented based on frequency-selective surface (FSS). The absorber is composed of polyvinyl chloride (PVC) layer, polyimide (PI) layer, and poly tetra fluoro ethylene (PTFE) layer, with a sandwich structure of PVC–PI–PTFE–metal plate. Periodic conductive patterns play a crucial role in the absorber, and in traditional, it is designed on the upper surface of PI layer to form LC resonance. Different from commonly absorber, all the patterns are located on the lower surface of the PI layer in this work, and hence the impedance matching and absorptivity are improved in this purposed absorber. The flexible absorber with patterns on lower surface of the PI layer is compared with that on upper surface of the PI layer, the difference and the reasons are explained by absorption mechanism based on equivalent circuit model, and surface current density and electric field distribution are used to analyze resonance peaks. Absorptivity is greater than 90% in a frequency range of 10.47 GHz–45.44 GHz with relative bandwidth of 125.1%, covering the whole Ku, K, Ka, and some of X, U bands, especially containing the whole K bands from 12 GHz to 40 GHz. Radar cross section (RCS) is reduced at least 10 dB in 11.48 GHz–43.87 GHz frequency ranges, and absorption remained about 90% when the incident angle changed from 0 ° to 55°. The purposed absorber is fabricated, measured, and experiment results show good agreement with theoretical analysis and numerical simulation. After bonded on outer surface of different cylinders with diameters of 200 mm and 100 mm, the absorption of MMA is approximately reduced 10% and 20% respectively, which shows good conformal character with surface of various curvatures. Due to the attractive performance on strong absorption in the whole K-bands, flexible and easy conformal, our design exhibits broad potential application in radar stealth and sensors.