A Frequency Selective Surface (FSS) based wideband reflective linear-cross and linear-circular polarization converter is proposed. The FSS consists of an H-shaped electric dipole loaded with capacitive patches printed on top of the low-loss dielectric spacer with the other side grounded. For the y/x linearly polarized wave incidence on the proposed design, the reflected wave is orthogonally polarized with a 90% Polarization Conversion Ratio (PCR) from 6.74-13.20 GHz, 15.96-17.20 GHz and 23.78-26.44 GHz. It is not only limited to that but also performs linear-circular conversion with 3-dB minimum Axial Ratio (AR) from 3.36-5.18 GHz, 17.80-21.80 GHz and 27.29-28.66 GHz. This design is highly miniaturized with a very compact structural periodicity of 0.034λL×0.040 λL and a low-profile thickness of 0.018λL, where λL is the free-space wavelength of the lowest operating frequency. Considerable stable performance is achieved for different oblique incidences. The simulated surface current patterns are investigated for top FSS and ground for multiple resonant frequencies. The dual-polarized linear-cross and linear-circular polarizing reflectors in a single design with distinct frequency bands would be ideal for dual operation based real-time applications. © 2023 IEEE.